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Taylor, Benjamin
SCALE manual
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authored
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Batson Iii, John
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CSAS5App.rst
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.. _CSAS5App:
CSAS5 Appendix A:
Additional Example Applications of CSAS5
========================================
==================
Additional Example Applications of CSAS5
========================================
Several example uses of CSAS5 are shown in this section for a variety of
applications. Note that many of these examples have been provided since
...
...
CSAS6App.rst
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.. _CSAS6App:
Additional Example Applications of CSAS6
========================================
Several example uses of CSAS6 are shown in this section for a variety of applications.
.. _runKENOCSAS6:
Run KENOVI using CSAS6

CSAS6 creates a microscopic working format library and a mixing table
that is passed to KENOVI. The library is created using
CENTRM/PMC/WORKER to process the cross section data in the resolved
resonance regions of the isotopes contained in the library. CSAS6 then
executes KENOVI, which calculates *k*\ :sub:`eff` for the problem. The
following examples are for using the multigroup mode of calculation for
KENOVI. Using the continuous energy mode can be accomplished by simply
changing the library name to one of the continuous energy libraries.
EXAMPLE 1. CSAS6 – Determine the *k*\ :sub:`eff` of a system.
Consider a problem consisting of eight uranium metal cylinders that are
93.2% wt enriched, having a density of 18.76 g/cm\ :sup:`3`. The
cylinders are arranged in a 2 × 2 × 2 array. Each has a radius of
5.748 cm and a height of 10.765 cm. The centertocenter spacing in the
horizontal (XY) plane is 13.74 cm and the vertical centertocenter
spacing is 13.01 cm. Because the cross section processing will be done
assuming an infinite homogeneous medium and no cell mixtures are used,
there is no unit cell data. The input data for this problem follow.
.. highlight:: scale
::
=CSAS6
SET UP 2C8 IN CSAS6
V7238
READ COMP
URANIUM 1 DEN=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 END
END COMP
READ PARAMETERS FLX=YES FDN=YES FAR=YES END PARAMETERS
READ GEOMETRY
UNIT 1
CYLINDER 10 5.748 5.3825 5.3825
CUBOID 20 6.87 6.87 6.87 6.87 6.505 6.505
MEDIA 1 1 10
MEDIA 0 1 20 10
BOUNDARY 20
GLOBAL UNIT 2
CUBOID 10 4P13.74 2P13.010
ARRAY 1 10 PLACE 1 1 1 6.87 6.87 6.505
BOUNDARY 10
END GEOMETRY
READ ARRAY
GBL=1 ARA=1 NUX=2 NUY=2 NUZ=2 FILL F1 END FILL
END ARRAY
END DATA
END
EXAMPLE 2. CSAS6 – Determine the *k*\ :sub:`eff` of an array of fuel pellets in
a UO\ :sub:`2`\ F\ :sub:`2` solution.
Consider a 60 cm inside diameter cylindrical tank filled with
5.0%enriched UO\ :sub:`2` fuel rods and 5.0%‑enriched
UO\ :sub:`2`\ F\ :sub:`2` solution at 295 gm/liter. A 51 × 51 × 1 array
of fuel rods is centered on the bottom of the tank. The fuel rods are
366 cm long, 0.45 cm in radius, clad with 0.01cmthick Al, and at a
pitch of 1.5 cm. The fuel rods sit on the bottom of the container and
the container and solution rise 5.0 cm above the top of the rods. The
container is 10 cm thick in the side and bottom and open at the top.
Determine the *k*\ :sub:`eff` of the system. Input data for this problem
follow.
::
=CSAS6
UO2 pins in a UO2F2 solution
V7238
READ COMP
UO2 1 0.95 300 92235 5.0 92238 95.0 END
AL 2 1.0 300 END
SOLNUO2F2 3 295 0.0 1.0 300 92235 5.0 92238 95.0 END
AL 4 1.0 300 END
SOLNUO2F2 5 295 0.0 1.0 300 92235 5.0 92238 95.0 END
END COMP
READ CELLDATA
LATTICECELL SQUAREPITCH PITCH=1.50 3 FUELD=0.9 1 CLADD=0.94 2 END
END CELLDATA
READ GEOM
UNIT 1
COM='FUEL PIN'
CYLINDER 10 0.45 2P183.0
CYLINDER 20 0.47 2P183.1
CUBOID 30 4P0.75 2P183.1
MEDIA 1 1 10
MEDIA 2 1 20 10
MEDIA 3 1 30 20 10
BOUNDARY 30
GLOBAL UNIT 2
COM='FUEL PINS AND SOLUTION IN TANK'
CUBOID 10 4p38.25 2P183.1
CYLINDER 20 60.0 188.1 183.1
CYLINDER 30 70.0 188.1 193.1
ARRAY 1 10 PLACE 26 26 1 3*0.0
MEDIA 5 1 20 10
MEDIA 4 1 30 20
BOUNDARY 30
END GEOM
READ ARRAY
ARA=1 NUX=51 NUY=51 NUZ=1 FILL F1 END FILL
END ARRAY
END DATA
END
Run KENOVI containing cellweighted mixtures

CSAS6 creates a microscopic working format library and a mixing table
that is passed to KENOVI. The microscopic cross sections of the
nuclides used in the unit cell geometry description are cell‑weighted by
specifying CELLMIX= followed by a unique mixture number. This mixture
number utilizes the cellweighted cross sections that represent the
heterogeneous system. CSAS6 executes KENOVI and calculates *k*\ :sub:`eff` for
the problem.
EXAMPLE 1. CSAS6 – Calculate the *k*\ :sub:`eff` of an array of fuel assemblies
using cellweighted cross sections.
Consider the 4 × 4 × 1 array of fuel assemblies in a square aluminum
cask described in Sect. 2.2.A.1.1, Example 2. Calculate the *k*\ :sub:`eff` of
the system by using the cellweighted mixture 200 to represent the fuel
pins in the fuel assembly. Note that mixtures 1, 2, and 3, representing
UO\ :sub:`2`, zirconium, and water, respectively, are used in the unit
cell description. Cellweighting is applied to the microscopic
cross sections that are used in the cell, making them incorrect for use
elsewhere. Because water is used both inside the cell and between the
fuel assemblies, an additional mixture, mixture 6, has been added to
represent the water between the fuel assemblies. The input data for this
problem follow.
::
=CSAS6
SQUARE FUEL CASK EXAMPLE USING HOMOGENEOUS MOCKUP
V7238
READ COMP
UO2 1 DEN=9.21 1.0 293. 92235 2.35 92238 97.65 END
ZR 2 1 END
H2O 3 1 END
B4C 4 0.367 END
AL 4 0.636 END
AL 5 1 END
H2O 6 1 END
END COMP
READ CELLDATA
LATTICECELL SQUAREPITCH PITCH=1.3 3 FUELD=0.8 1 CLADD=0.94 2 CELLMIX=200 END
END CELLDATA
READ PARAM FAR=YES GEN=253 END PARAM
READ GEOM
UNIT 2
COM='FUEL ASSEMBLY'
CUBOID 10 4P11.05 2P183.07
CUBOID 20 4P11.70 2P183.72
CUBOID 30 4P12.20 2P184.22
MEDIA 200 1 10
MEDIA 4 1 20 10
MEDIA 6 1 30 20 10
BOUNDARY 30
GLOBAL UNIT 3
COM='FUEL CASK CONTAINING 4X4 ARRAY OF ASSEMBLIES'
CUBOID 10 4P48.8 2P184.22
CUBOID 20 4P58.8 2P194.22
ARRAY 1 10 PLACE 1 1 1 36.6 36.6 0.0
MEDIA 5 1 20 10
BOUNDARY 20
END GEOM
READ ARRAY
ARA=1 NUX=4 NUY=4 NUZ=1 FILL F2 END FILL
END ARRAY
END DATA
END
EXAMPLE 2. CSAS6 – Determine the *k*\ :sub:`eff` of an array of fuel pellets in
a UO\ :sub:`2`\ F\ :sub:`2` solution using cell‑weighted cross sections.
This is the same problem as described in :ref:`runKENOCSAS6` Example 2.
However, the rods and solutions have been replaced with a cellweighted
mixture 50. Determine the *k*\ :sub:`eff` of the container. Input data for this
problem follow.
::
=CSAS6
UO2 pins in a UO2F2 solution, cellweighted mixture
V7238
READ COMP
UO2 1 0.95 300 92235 5.0 92238 95.0 END
AL 2 1.0 300 END
SOLNUO2F2 3 295 0.0 1.0 300 92235 5.0 92238 95.0 END
AL 4 1.0 300 END
SOLNUO2F2 5 295 0.0 1.0 300 92235 5.0 92238 95.0 END
END COMP
READ CELLDATA
LATTICECELL SQUAREPITCH PITCH=1.50 3 FUELD=0.9 1 CLADD=0.94 2 CELLMIX=50 END
END CELLDATA
READ GEOM
GLOBAL UNIT 2
COM='FUEL PINS AND SOLUTION IN TANK'
CUBOID 10 4p38.25 2P183.1
CYLINDER 20 60.0 188.1 183.1
CYLINDER 30 70.0 188.1 193.1
MEDIA 50 1 10
MEDIA 5 1 20 10
MEDIA 4 1 30 20
BOUNDARY 30
END GEOM
END DATA
END
Run KENOVI containing multiple unit cells

CSAS6 can create a microscopic working format library and a mixing table
that contains more than one unit cell. Each unit cell is explicitly
defined in the CELLDATA section of the standard composition data.
Materials may appear in only one unit cell. All materials in the
standard composition that are not contained in a unit cell are processed
assuming infinite homogeneous media. CSAS6 passes the created working
library to KENOVI which calculates *k*\ :sub:`eff` for the problem.
EXAMPLE 1. CSAS6 – Calculate the *k*\ :sub:`eff` of a system using two unit
cell descriptions.
Consider an infinite XYarray composed of two types of fuel assemblies
in a checkerboard pattern moderated by water. Each assembly consists of
a 17 × 17 × 1 array of zirconiumclad, enriched UO\ :sub:`2` fuel pins
in a square pitched array. In one array the uranium is 3.5%enriched and
in the other array the uranium is 2.9%enriched. The UO\ :sub:`2` has a
density of 9.21 g/cm\ :sup:`3`. The pin diameter is 0.8 cm and is 366 cm
long. The clad is 0.07 cm thick, and the pitch is 1.3 cm. Each fuel
bundle is contained in a 0.65cmthick Boral sheath. The bundles are
separated by an edgetoedge spacing of 1.0 cm. The water and zirconium
is input in the standard composition data once for every unit cell in
which it appears because a material may appear in only one unit cell.
Determine the *k*\ :sub:`eff` of the infinite array. Note that periodic
boundary conditions are required to obtain an infinite checkerboard
array. Input data for this problem follow.
::
=CSAS6
2 SQUARE FUEL ASSEMBLIES EXAMPLE IN AN INFINITE LATTICE OF ASSEMBLIES
V7238
READ COMP
UO2 1 DEN=9.21 1.0 293. 92235 3.5 92238 96.5 END
ZR 2 1 END
H2O 3 1 END
UO2 4 DEN=9.21 1.0 293. 92235 2.9 92238 97.1 END
ZR 5 1 END
H2O 6 1 END
B4C 7 0.367 END
AL 7 0.636 END
END COMP
READ CELLDATA
LATTICECELL SQUAREPITCH PITCH=1.3 3 FUELD=0.8 1 CLADD=0.94 2 END
LATTICECELL SQUAREPITCH PITCH=1.3 6 FUELD=0.8 4 CLADD=0.94 5 END
END CELLDATA
READ PARAM FAR=YES GEN=253 END PARAM
READ GEOM
UNIT 1
COM='3.5 W% FUEL PIN'
CYLINDER 10 0.4 2P183.0
CYLINDER 20 0.47 2P183.07
CUBOID 30 4P0.65 2P183.07
MEDIA 1 1 10
MEDIA 2 1 20 10
MEDIA 3 1 30 20 10
BOUNDARY 30
UNIT 2
COM='3.5 W% FUEL ASSEMBLY'
CUBOID 10 4P11.05 2P183.07
CUBOID 20 4P11.7 2P183.72
CUBOID 30 4P12.2 2P184.22
ARRAY 1 10 PLACE 9 9 1 3*0.0
MEDIA 7 1 20 10
MEDIA 3 1 20 20 20
BOUNDARY 30
UNIT 3
COM='2.9 W% FUEL PIN'
CYLINDER 10 0.4 2P183.0
CYLINDER 20 0.47 2P183.07
CUBOID 30 4P0.65 2P183.07
MEDIA 4 1 10
MEDIA 5 1 20 10
MEDIA 6 1 30 20 10
BOUNDARY 30
UNIT 4
COM='2.9 W% FUEL ASSEMBLY'
CUBOID 10 4P11.05 2P183.07
CUBOID 20 4P11.7 2P183.72
CUBOID 30 4P12.2 2P184.22
ARRAY 2 10 PLACE 9 9 1 3*0.0
MEDIA 7 1 20 10
MEDIA 6 1 20 20 20
BOUNDARY 30
GLOBAL UNIT 5
COM='FUEL CASK CONTAINING 4X4 ARRAY OF ASSEMBLIES'
CUBOID 10 4P24.4 2P184.22
ARRAY 3 10 PLACE 1 1 1 12.2 12.2 0.0
BOUNDARY 10
END GEOM
READ ARRAY
ARA=1 NUX=17 NUY=17 NUZ=1 FILL F1 END FILL
ARA=2 NUX=17 NUY=17 NUZ=1 FILL F3 END FILL
GBL=3 ARA=3 NUX=2 NUY=2 NUZ=1 FILL 2 4 4 2 END FILL
END ARRAY
READ BOUNDS XYF=PERIODIC END BOUNDS
END DATA
END
EXAMPLE 2. CSAS6 – Calculate the *k*\ :sub:`eff` of a system using two unit
cell descriptions and cellweighted mixtures.
Consider a problem in which a stainless steel cylinder with an inner
diameter of 56 cm and an inside height of 91 cm is filled with pellets
of UO\ :sub:`2` in borated water. The steel is 0.125 cm thick. The
spherical 2.57%enriched UO\ :sub:`2` pellets have a diameter of 1.07 cm
and are arranged in a triangular pitch array with a pitch of 1.13 cm.
The spherical 2.96%enriched UO\ :sub:`2` pellets have a diameter of
1.07 cm and are arranged in a triangular pitch array with a pitch of
1.12 cm. The cylindrical tank is filled half full of the 2.96% pellets
in borated water, and the remainder is filled with the 2.57%enriched
pellets in borated water.
Mixture 100 is the cellweighted mixture containing the 2.57%enriched
uranium pellets and mixture 200 is the cellweighted mixture containing
the 2.96%enriched uranium pellets. Determine the *k*\ :sub:`eff` of this
system. Input data for this problem follow.
::
=CSAS6
2.57% AND 2.96% ENR UO2 PELLETS IN 3500 PPM BORATED WATER
V7238
READ COMP
UO2 1 0.925 283 92235 2.57 92238 97.43 END
H2O 2 1.0 283 END
ATOMBACID 2 2.00172 3 5000 1 1001 3 8016 3 1.0 283 END
UO2 3 0.925 283 92235 2.96 92238 97.04 END
H2O 4 1.0 283 END
ATOMBACID 4 2.00172 3 5000 1 1001 3 8016 3 1.0 283 END
SS304 5 1.0 283 END
END COMP
READ CELLDATA
LATTICECELL CELLMIX=100 SPHTRIANGP PITCH=1.13 2 FUELD=1.07 1 END
LATTICECELL CELLMIX=200 SPHTRIANGP PITCH=1.13 4 FUELD=1.07 3 END
END CELLDATA
READ PARAM FLX=YES END PARAM
READ GEOM
GLOBAL UNIT 1
CYLINDER 10 38.0 45.5 0.0
CYLINDER 20 38.0 91.0 0.0
CYLINDER 30 38.125 91.0 0.125
MEDIA 100 1 10
MEDIA 200 1 20 10
MEDIA 5 1 30 20
BOUNDARY 30
END GEOM
END DATA
END
DEVC.rst
0 → 100644
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aa9d21a0
..
_DEVC
:
DEVC
:
Denovo
EigenValue
Calculation
===================================
*
Douglas
E
.
Peplow
and
Cihangir
Celik
*
Introduction

The
DEVC
(
Denovo
EigenValue
Calculation
)
sequence
is
an
interface
to
the
Denovo
discrete

ordinates
package
:
cite
:`
evans_denovo_2010
`
for
calculating
criticality
eigenvalue
problems
.
This
sequence
reads
an
input
file
very
similar
to
a
CSAS6
input
file
:
cite
:`
goluoglu_monte_2011
`
that
contains
an
extra
block
of
input
for
describing
the
Denovo
mesh
grid
and
calculational
parameters
.
Many
of
the
subroutines
are
shared
from
the
MAVRIC
routines
that
interface
with
Denovo
for
fixed

source
calculations
.
This
manual
assumes
that
the
user
is
familiar
with
the
discrete

ordinates
method
for
radiation
transport
and
the
Denovo
package
.
DEVC
provides
an
easy
way
for
users
to
modify
existing
CSAS6
inputs
and
use
them
to
run
Denovo
.
The
DEVC
sequence
also
provides
a
way
to
create
mesh
geometry
for
Denovo
from
the
combinatorial
solid
geometry
description
used
by
KENO

VI
.
The
steps
in
the
DEVC
sequence
are
listed
in
:
numref
:`
tab2

4
a

1
`.
..
_tab2

4
a

1
:
..
table
::
Steps
in
DEVC
for
an
input
file
named
*
input
*.
inp
:
align
:
center
+++++

Step

Module
/
Task

Creates
file

To
stop
after

+=================+=================+=================+=================+

0

Check
user





input



+++++





+++++

1

Self

shielding





(
celldata
/
cellm





ix
)





calculations



+++++





+++++

2

Produces





optional
\*.
png





plots



+++++


Produces


``
parm
=
check
``



optional





\*
.3
mdap
files





(
to
visualize





grid
in





MeshFileViewer
)



+++++





+++++

3

Creates
AMPX

``
ft02f001
``

``
parm
=
cross
``



cross
sections





for
the
“
real
”





materials



+++++





+++++

4

Creates
Denovo

``
xkba_b
.
inp
``

``
parm
=
input
``



binary
stream





input
file
and

``
input
.
mmt
``




the










macromaterial





table
file



+++++





+++++

5

Runs
Denovo
to

``
input
.
dff
``
or




compute





:
math
:`
k_
{

``
input
.
dso
``




\
text
{
eff
}}`





and





either
the





fluxes
or
the





fission
source



+++++
The
DEVC
sequence
uses
KENO

VI
geometry
.
Users
can
specify
what
output
Denovo
will
generate
:
fluxes
by
space
and
energy
in
a
binary
\*.
dff
(
Denovo
flux
file
)
file
or
the
space

only
fission
source
distribution
in
a
binary
\*.
dso
(
Denovo
spatial
output
)
file
.
The
eigenvalue
is
printed
in
the
main
output
text
file
.
Some
of
the
more
common
KENO
starting
source
types
are
supported
.
Other
starting
source
types
may
be
added
or
extended
to
all
of
the
different
array
types
in
the
future
.
Currently
,
starting
sources
are
not
sent
to
Denovo
because
the
Arnoldi
solver
does
not
use
it
.
This
may
change
in
the
future
.
Sequence
input

The
input
file
for
a
DEVC
calculation
looks
similar
to
a
CSAS6
input
file
,
as
shown
in
:
numref
:`
tab2

4
a

2
`.
The
major
difference
is
that
the
parameter
block
contains
information
for
the
Denovo
calculation
,
not
the
KENO
Monte
Carlo
calculation
.
A
macromaterial
block
is
used
to
describe
how
the
KENO

VI
materials
are
mapped
onto
the
Denovo
mesh
grid
.
Only
multi

group
cross

section
libraries
can
be
used
with
Denovo
.
..
list

table
::
Input
file
for
a
DEVC
calculation
(
and
differences
with
a
CSAS6
input
file
,
where
black
text
is
the
same
as
CSAS6
and
green
text
is
new
for
DEVC
sequence
)
:
name
:
tab2

4
a

2
:
align
:
center
*

..
image
::
figs
/
DEVC
/
tab2
.
png
Parameters
block
~~~~~~~~~~~~~~~~
This
block
contains
the
parameters
for
the
Denovo
eigenvalue
calculation
,
the
grid
geometry
,
and
the
macromaterials
.
Boundary
conditions
listed
in
the
parameters
block
will
override
those
listed
in
the
bounds
block
(
using
CSAS6
syntax
).
:
numref
:`
tab2

4
a

3
`
lists
the
Denovo
calculation
parameters
and
their
default
values
,
and
:
numref
:`
tab2

4
a

4
`
lists
the
keywords
for
the
setting
the
boundary
conditions
and
file
saving
options
.
The
grid
geometry
is
defined
in
a
sub

block
in
the
parameters
block
,
or
the
keyword
``
“
gridGeometryID
=\
*
n
*\
”
``
can
be
used
to
point
to
a
grid
geometry
defined
in
its
own
input
block
.
..
list

table
::
Denovo
parameters
in
the
parameters
block
:
align
:
center
:
name
:
tab2

4
a

3
*

..
image
::
figs
/
DEVC
/
tab3
.
png
..
list

table
::
Boundary
conditions
and
what
type
of
file
to
save
:
align
:
center
:
name
:
tab2

4
a

4
*

..
image
::
figs
/
DEVC
/
tab4
.
png
Grid
geometry
block
~~~~~~~~~~~~~~~~~~~
Grid
geometries
(
“
``
gridGeometry
``
*
id
*\
”
)
require
an
identification
number
and
then
a
description
of
a
three

dimensional
rectangular
mesh
by
specifying
the
bounding
planes
of
the
cells
in
each
of
the
*
x
*,
*
y
*,
and
*
z
*
dimensions
.
The
keyword
``
“
xPlanes
…
end
”
``
can
be
used
to
list
plane
values
(
in
any
order
).
The
keyword
“
``
xLinear
``
*
n
*
*
a
*
*
b
*\
”
can
be
used
to
specify
*
n
*
cells
between
*
a
*
and
*
b
*.
The
keywords
“
``
xPlanes
``
”
and
``
“
xLinear
”
``
can
be
used
together
and
multiple
times
–
they
will
simply
add
planes
to
any
already
defined
for
that
dimension
.
Any
duplicate
planes
will
be
removed
.
Similar
keywords
are
used
for
the
*
y
*
and
*
z
*
dimensions
.
When
using
multiple
instances
of
the
keywords
\*``
Linear
``
and
\*``
Planes
``
for
a
given
dimension
,
duplicates
should
be
removed
from
the
final
list
.
In
some
cases
,
double
precision
math
will
leave
two
planes
that
are
nearly
identical
but
not
removed
(
e
.
g
.,
6.0
and
5.9999999
).
To
prevent
this
,
a
default
tolerance
is
set
to
remove
planes
that
are
within
10
\
:
sup
:`
6
`
cm
of
each
other
.
The
user
is
free
to
change
this
by
using
the
keyword
``
“
tolerance
=
”
``
and
specifying
something
else
.
Note
that
the
tolerance
can
be
reset
to
a
different
value
in
between
each
use
of
\*``
Linear
``
or
\*``
Planes
``.
The
keyword
“
``
make3dmap
``
”
for
a
particular
grid
geometry
definition
will
create
a
file
called
“
\
*
outputName
*.
grid
\
*
id
*
.3
dmap
”
,
which
can
be
visualized
using
the
Java
Mesh
File
Viewer
.
These
files
will
contain
crude
geometry
information
(
unit
,
region
,
material
)
that
corresponds
to
the
center
of
each
voxel
.
Keywords
for
the
grid
geometry
block
are
listed
in
:
numref
:`
tab2

4
a

5
`.
..
list

table
::
Grid
geometry
input
keywords
:
align
:
center
:
name
:
tab2

4
a

5
*

..
image
::
figs
/
DEVC
/
tab5
.
png
Macromaterial
block
~~~~~~~~~~~~~~~~~~~
In
order
to
get
more
accurate
solutions
from
a
coarse

mesh
discrete

ordinates
calculation
,
Denovo
can
represent
the
material
in
each
voxel
of
the
mesh
as
a
volume

weighted
mixture
of
the
real
materials
in
the
problem
.
When
constructing
the
Denovo
input
,
DEVC
can
estimate
the
volume
fraction
taken
by
each
real
material
in
each
voxel
by
a
sampling
method
.
The
user
can
specify
parameters
for
how
to
sample
the
geometry
.
Note
that
finer
sampling
makes
more
accurate
estimates
of
the
material
fraction
but
requires
more
setup
time
to
create
the
Denovo
input
.
Users
should
understand
how
the
macromaterials
are
sampled
and
consider
that
when
constructing
a
mesh
grid
.
This
is
especially
important
for
geometries
that
contain
arrays
.
Careful
consideration
should
be
given
when
overlaying
a
mesh
on
a
geometry
that
contains
arrays
of
arrays
.
Because
the
list
of
macromaterials
could
become
large
,
the
user
can
also
specify
a
tolerance
for
how
close
two
different
macromaterials
can
be
to
be
considered
the
same
,
thereby
reducing
the
total
number
of
macromaterials
.
The
macromaterial
tolerance
,
``
“
mmTolerance
=
”
``,
is
used
for
creating
a
different
macromaterial
from
the
ones
already
created
by
looking
at
the
infinity
norm
between
two
macromaterials
.
The
number
of
macromaterials
does
not
appreciably
impact
Denovo
run
time
or
memory
requirements
.
Keywords
for
the
macromaterial
block
are
listed
:
numref
:`
tab2

4
a

6
`.
Two
different
sampling
methods
are
available
–
ray
tracing
:
cite
:`
ibrahim_improving_2009
`
with
the
keyword
``
mmRayTest
``
and
point
testing
:
cite
:`
johnson_fast_2013
`
with
the
keyword
``
mmPointTest
``.
..
list

table
::
Macromaterial
block
input
:
align
:
center
:
name
:
tab2

4
a

6
*

..
image
::
figs
/
DEVC
/
tab6
.
png
Ray
tracing
^^^^^^^^^^^
This
method
estimates
the
volume
of
different
materials
in
the
Denovo
mesh
grid
elements
by
throwing
rays
through
the
KENO

VI
geometry
and
computing
the
average
track
lengths
through
the
each
material
.
Rays
are
traced
in
all
three
dimensions
to
better
estimate
the
volume
fractions
of
materials
within
each
voxel
.
The
``
mmSubCell
``
parameter
controls
how
many
rays
to
trace
in
each
voxel
in
each
dimension
.
For
example
,
if
``
mmSubCell
=``\
:
math
:`\
text
{\
n
}`,
then
when
tracing
rays
in
the
*
z
*
dimension
,
each
column
of
voxels
uses
a
set
of
:
math
:`
n
\
times
n
`
rays
starting
uniformly
spaced
in
the
*
x
*
and
*
y
*
dimensions
.
With
rays
being
cast
from
all
three
orthogonal
directions
,
then
a
total
of
:
math
:`
3
n
^{
2
}`
rays
are
used
to
sample
each
voxel
.
One
can
think
of
subcells
as
an
equally
spaced
sub

mesh
with
a
single
ray
positioned
at
each
center
.
The
number
of
subcells
in
each
direction
,
and
hence
the
number
of
rays
,
can
be
explicitly
given
with
``
mmSubCells
ny
nz
nx
nz
nx
ny
end
``
keyword
for
rays
parallel
to
the
:
math
:`
x
`
axis
,
:
math
:`
y
`
axis
,
and
:
math
:`
z
`
axis
.
:
numref
:`
fig2

4
a

1
`
shows
different
subcell
configurations
(
in
two
dimensions
)
for
a
given
voxel
.
..
_fig2

4
a

1
:
..
figure
::
figs
/
DEVC
/
fig1
.
png
:
align
:
center
:
width
:
500
</