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  <div class="section" id="devc-denovo-eigenvalue-calculation">
<span id="devc"></span><h1>DEVC: Denovo EigenValue Calculation<a class="headerlink" href="#devc-denovo-eigenvalue-calculation" title="Permalink to this headline"></a></h1>
<p><em>Douglas E. Peplow and Cihangir Celik</em></p>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
<p>The DEVC (Denovo EigenValue Calculation) sequence is an interface to the
Denovo discrete-ordinates package <a class="bibtex reference internal" href="appendixc.html#evans-denovo-2010" id="id1">[ESSC10]</a> for calculating criticality
eigenvalue problems. This sequence reads an input file very similar to a
CSAS6 input file <a class="bibtex reference internal" href="Sourcerer.html#goluoglu-monte-2011" id="id2">[GPJD+11]</a> 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.</p>
<p>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.</p>
<p>The steps in the DEVC sequence are listed in <a class="reference internal" href="#tab2-4a-1"><span class="std std-numref">Table 24</span></a>.</p>
<span id="tab2-4a-1"></span><table class="docutils align-center" id="id5">
<caption><span class="caption-number">Table 24 </span><span class="caption-text">Steps in DEVC for an input file named <em>input</em>.inp</span><a class="headerlink" href="#id5" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Step</p></th>
<th class="head"><p>Module/Task</p></th>
<th class="head"><p>Creates file</p></th>
<th class="head"><p>To stop after</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>0</p></td>
<td><p>Check user
input</p></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p>1</p></td>
<td><p>Self-shielding
(celldata/cellm
ix)
calculations</p></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p>2</p></td>
<td><p>Produces
optional *.png
plots</p></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Produces
optional
*.3mdap files
(to visualize
grid in
MeshFileViewer)</p></td>
<td></td>
<td><p><code class="docutils literal notranslate"><span class="pre">parm=check</span></code></p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>3</p></td>
<td><p>Creates AMPX
cross sections
for the “real”
materials</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ft02f001</span></code></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">parm=cross</span></code></p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>4</p></td>
<td><p>Creates Denovo
binary stream
input file and
the</p>
<p>macromaterial
table file</p>
</td>
<td><p><code class="docutils literal notranslate"><span class="pre">xkba_b.inp</span></code></p>
<p><code class="docutils literal notranslate"><span class="pre">input.mmt</span></code></p>
</td>
<td><p><code class="docutils literal notranslate"><span class="pre">parm=input</span></code></p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>5</p></td>
<td><p>Runs Denovo to
compute
<span class="math notranslate nohighlight">\(k_{
\text{eff}}\)</span>
and
either the
fluxes or the
fission source</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">input.dff</span></code> or</p>
<p><code class="docutils literal notranslate"><span class="pre">input.dso</span></code></p>
</td>
<td></td>
</tr>
</tbody>
</table>
<p>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.</p>
<p>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.</p>
</div>
<div class="section" id="sequence-input">
<h2>Sequence input<a class="headerlink" href="#sequence-input" title="Permalink to this headline"></a></h2>
<p>The input file for a DEVC calculation looks similar to a CSAS6 input
file, as shown in <a class="reference internal" href="#tab2-4a-2"><span class="std std-numref">Table 25</span></a>. 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.</p>
<table class="docutils align-center" id="tab2-4a-2">
<caption><span class="caption-number">Table 25 </span><span class="caption-text">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)</span><a class="headerlink" href="#tab2-4a-2" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 100%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><img alt="_images/tab2.png" src="_images/tab2.png" />
</td>
</tr>
</tbody>
</table>
<div class="section" id="parameters-block">
<h3>Parameters block<a class="headerlink" href="#parameters-block" title="Permalink to this headline"></a></h3>
<p>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). <a class="reference internal" href="#tab2-4a-3"><span class="std std-numref">Table 26</span></a> lists the Denovo
calculation parameters and their default values, and <a class="reference internal" href="#tab2-4a-4"><span class="std std-numref">Table 27</span></a> 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 <code class="docutils literal notranslate"><span class="pre">“gridGeometryID=\</span> <span class="pre">*n*\</span> <span class="pre"></span></code> can be used to point to a
grid geometry defined in its own input block.</p>
<table class="docutils align-center" id="tab2-4a-3">
<caption><span class="caption-number">Table 26 </span><span class="caption-text">Denovo parameters in the parameters block</span><a class="headerlink" href="#tab2-4a-3" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 100%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><img alt="_images/tab3.png" src="_images/tab3.png" />
</td>
</tr>
</tbody>
</table>
<table class="docutils align-center" id="tab2-4a-4">
<caption><span class="caption-number">Table 27 </span><span class="caption-text">Boundary conditions and what type of file to save</span><a class="headerlink" href="#tab2-4a-4" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 100%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><img alt="_images/tab4.png" src="_images/tab4.png" />
</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="grid-geometry-block">
<h3>Grid geometry block<a class="headerlink" href="#grid-geometry-block" title="Permalink to this headline"></a></h3>
<p>Grid geometries (“<code class="docutils literal notranslate"><span class="pre">gridGeometry</span></code> <em>id</em>”) 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 <em>x</em>, <em>y</em>, and
<em>z</em> dimensions. The keyword <code class="docutils literal notranslate"><span class="pre">“xPlanes</span> <span class="pre"></span> <span class="pre">end”</span></code> can be used to list plane
values (in any order). The keyword “<code class="docutils literal notranslate"><span class="pre">xLinear</span></code> <em>n</em> <em>a</em> <em>b</em>” can be used
to specify <em>n</em> cells between <em>a</em> and <em>b</em>. The keywords “<code class="docutils literal notranslate"><span class="pre">xPlanes</span></code>” and
<code class="docutils literal notranslate"><span class="pre">“xLinear”</span></code> 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 <em>y</em> and <em>z</em>
dimensions.</p>
<p>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</sup>
cm of each other. The user is free to change this by using the keyword
<code class="docutils literal notranslate"><span class="pre">“tolerance=”</span></code> and specifying something else. Note that the tolerance can
be reset to a different value in between each use of *``Linear`` or
*``Planes``.</p>
<p>The keyword “<code class="docutils literal notranslate"><span class="pre">make3dmap</span></code>” for a particular grid geometry definition will
create a file called “<em>outputName</em>.grid<em>id</em>.3dmap”, 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.</p>
<p>Keywords for the grid geometry block are listed in <a class="reference internal" href="#tab2-4a-5"><span class="std std-numref">Table 28</span></a>.</p>
<table class="docutils align-center" id="tab2-4a-5">
<caption><span class="caption-number">Table 28 </span><span class="caption-text">Grid geometry input keywords</span><a class="headerlink" href="#tab2-4a-5" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 100%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><img alt="_images/tab5.png" src="_images/tab5.png" />
</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="macromaterial-block">
<h3>Macromaterial block<a class="headerlink" href="#macromaterial-block" title="Permalink to this headline"></a></h3>
<p>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.</p>
<p>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, <code class="docutils literal notranslate"><span class="pre">“mmTolerance=”</span></code>, is used for
creating a different macromaterial from the ones already created by
looking at the infinity norm between two macromaterials.</p>
<p>The number of macromaterials does not appreciably impact Denovo run time
or memory requirements.</p>
<p>Keywords for the macromaterial block are listed <a class="reference internal" href="#tab2-4a-6"><span class="std std-numref">Table 29</span></a>. Two
different sampling methods are available – ray tracing <a class="bibtex reference internal" href="MAVRIC.html#ibrahim-improving-2009" id="id3">[IPE+09]</a> with the
keyword <code class="docutils literal notranslate"><span class="pre">mmRayTest</span></code> and point testing <a class="bibtex reference internal" href="MAVRIC.html#johnson-fast-2013" id="id4">[Joh13]</a> with the keyword <code class="docutils literal notranslate"><span class="pre">mmPointTest</span></code>.</p>
<table class="docutils align-center" id="tab2-4a-6">
<caption><span class="caption-number">Table 29 </span><span class="caption-text">Macromaterial block input</span><a class="headerlink" href="#tab2-4a-6" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 100%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><img alt="_images/tab6.png" src="_images/tab6.png" />
</td>
</tr>
</tbody>
</table>
<div class="section" id="ray-tracing">
<h4>Ray tracing<a class="headerlink" href="#ray-tracing" title="Permalink to this headline"></a></h4>
<p>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 <code class="docutils literal notranslate"><span class="pre">mmSubCell</span></code> parameter controls how
many rays to trace in each voxel in each dimension. For example, if
<code class="docutils literal notranslate"><span class="pre">mmSubCell=</span></code><span class="math notranslate nohighlight">\(\text{\ n}\)</span>, then when tracing rays in the
<em>z</em> dimension, each column of voxels uses a set of <span class="math notranslate nohighlight">\(n \times n\)</span>
rays starting uniformly spaced in the <em>x</em> and <em>y</em> dimensions. With rays
being cast from all three orthogonal directions, then a total of
<span class="math notranslate nohighlight">\(3n^{2}\)</span> 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 <code class="docutils literal notranslate"><span class="pre">mmSubCells</span> <span class="pre">ny</span> <span class="pre">nz</span> <span class="pre">nx</span> <span class="pre">nz</span> <span class="pre">nx</span>
<span class="pre">ny</span> <span class="pre">end</span></code> keyword for rays parallel to the <span class="math notranslate nohighlight">\(x\)</span> axis, <span class="math notranslate nohighlight">\(y\)</span> axis,
and <span class="math notranslate nohighlight">\(z\)</span> axis. <a class="reference internal" href="#fig2-4a-1"><span class="std std-numref">Fig. 27</span></a> shows different subcell
configurations (in two dimensions) for a given voxel.</p>
<div class="figure align-center" id="id6">
<span id="fig2-4a-1"></span><a class="reference internal image-reference" href="_images/fig14.png"><img alt="_images/fig14.png" src="_images/fig14.png" style="width: 500px;" /></a>
<p class="caption"><span class="caption-number">Fig. 27 </span><span class="caption-text">Ray positions within a voxel with different mmSubCells parameters.</span><a class="headerlink" href="#id6" title="Permalink to this image"></a></p>
</div>
<p>Ray tracing is a more robust method compared to the simple point testing
method used in previous versions of SCALE/MAVRIC; however, it requires
more memory than point testing. Ray tracing gives more accurate
estimates of volume fractions because track lengths across a voxel give
more information than a series of test points. Ray tracing is also much
faster than point testing because the particle tracking routines are
optimized for quickly determining lists of materials and distance along
a given ray.</p>
<p>Ray tracing operates on the grid geometry supplied by the user and
shoots rays in all three directions starting from the lower bounds of
the mesh grid. An example of arbitrary assembly geometry is shown in
<a class="reference internal" href="#fig2-4a-2"><span class="std std-numref">Fig. 28</span></a>. A ray consists of a number of steps that corresponds to
crossing a different material along the path of the ray. Ratios of each
step’s length to the voxel length in the ray’s direction determine the
material volume fraction of that step in that voxel, and summation of
the same material volume fractions gives the material volume fraction of
that material in that voxel. Ray tracing through a single voxel that
contains a fuel pin is illustrated in <a class="reference internal" href="#fig2-4a-3"><span class="std std-numref">Fig. 29</span></a>.</p>
<div class="figure align-center" id="id7">
<span id="fig2-4a-2"></span><a class="reference internal image-reference" href="_images/fig23.png"><img alt="_images/fig23.png" src="_images/fig23.png" style="width: 600px;" /></a>
<p class="caption"><span class="caption-number">Fig. 28 </span><span class="caption-text">Geometry model (left) and the Denovo representation (right) of an assembly using macromaterials determined by ray tracing.</span><a class="headerlink" href="#id7" title="Permalink to this image"></a></p>
</div>
<p>The final constructed macromaterials for this model are also shown in
<a class="reference internal" href="#fig2-4a-2"><span class="std std-numref">Fig. 28</span></a>. Voxels that contain only a single material are assigned
that original material number in the constructed macromaterials. For the
voxels that contain a fuel pin with three different materials, the
result is a new macromaterial consisting of the volume weighted
fractions of each original material.</p>
<p>After the rays are shot in all three directions, the material volume
fractions are updated and macromaterials are created by using these
material volume fractions. Material volume fraction calculations for a
single voxel, as shown in <a class="reference internal" href="#fig2-4a-3"><span class="std std-numref">Fig. 29</span></a>, are given by</p>
<div class="math notranslate nohighlight">
\[\begin{split}F_{m} = \ \sum_{d = x,y,z}^{}{\sum_{r = 1}^{N_{r}}{\sum_{s = 1}^{N_{s}}\left\{ \begin{matrix}
\frac{L_{d,r,s}}{L_{d}},\ \ \ &amp; m_{s} = = m \\
0,\ \ \ &amp; \mathrm{\text{otherwise}} \\
\end{matrix} \right.\ }} \ \ \ \ \ \  \mathrm{\text{ and  }} \ \ \ \ \ \ \ V_{m} = \frac{F_{m}}{\sum_{n = 1}^{N_{m}}F_{n}}\ ,\end{split}\]</div>
<p>where <em>F</em><sub>m</sub> = sampled fraction of material <em>m</em> in the voxel,</p>
<p><em>d</em> = direction of the rays (<em>x</em>, <em>y</em>, <em>z</em>),</p>
<p><em>r</em> = ray number,</p>
<p><em>N</em><sub>r</sub> = total number of rays in the voxel for direction of <em>d,</em></p>
<p><em>s</em> = step number,</p>
<p><em>N</em><sub>s</sub> = total number of steps for ray <em>r</em> in the voxel for direction of
<em>d,</em></p>
<p><em>L</em><sub>d,r,s</sub> = length of the steps <em>s</em> for ray <em>r</em> in the voxel for
direction of <em>d,</em></p>
<p><em>L</em><sub>d,</sub> = length of the voxel along direction of <em>d,</em></p>
<p><em>m</em><sub>s</sub> = material of step <em>s,</em></p>
<p><em>m</em> = material number,</p>
<p><em>N</em><sub>m</sub> = total number of materials in the voxel, and</p>
<p><em>V</em><sub>m</sub> = volume fraction of material <em>m</em> in the voxel.</p>
<div class="figure align-center" id="id8">
<span id="fig2-4a-3"></span><a class="reference internal image-reference" href="_images/fig33.png"><img alt="_images/fig33.png" src="_images/fig33.png" style="width: 400px;" /></a>
<p class="caption"><span class="caption-number">Fig. 29 </span><span class="caption-text">Ray tracing (in two dimensions) through a voxel.</span><a class="headerlink" href="#id8" title="Permalink to this image"></a></p>
</div>
</div>
<div class="section" id="point-testing">
<h4>Point testing<a class="headerlink" href="#point-testing" title="Permalink to this headline"></a></h4>
<p>The recursive bisection method uses a series of point tests to determine
the macromaterial fractions. For a given voxel, the material at the
center is compared to the material at the eight corners. If they are all
the same, the entire volume is considered to be made of that material.
If different, the volume is divided into two in each dimension. Each
subvolume is tested, and the method is then applied to the subvolumes
that are not of a single material. When the ratio of the volume of the
tested region to the original voxel becomes less than a user-specified
tolerance (in the range of 10<sup>-1</sup> to 10<sup>-4</sup>), then further
subdivision and testing are stopped. This is illustrated in
<a class="reference internal" href="#fig2-4a-4"><span class="std std-numref">Fig. 30</span></a>.</p>
<div class="figure align-center" id="id9">
<span id="fig2-4a-4"></span><a class="reference internal image-reference" href="_images/fig42.png"><img alt="_images/fig42.png" src="_images/fig42.png" style="width: 600px;" /></a>
<p class="caption"><span class="caption-number">Fig. 30 </span><span class="caption-text">Progression of the recursive bisection method (from upper left to lower right).</span><a class="headerlink" href="#id9" title="Permalink to this image"></a></p>
</div>
<p>In point testing, the keyword “<code class="docutils literal notranslate"><span class="pre">mmTolerance=</span></code><em>f</em>” is interpreted to be
where <em>f</em> is the smallest fraction of the voxel volume to consider. This
same tolerance <em>f</em> is also used to limit the number of macromaterials.
Before a new macromaterial is created, if one already exists where the
fraction of each actual material matches to within the given tolerance,
then the existing material will be used. If using only a single point at
the center of each voxel, use <code class="docutils literal notranslate"><span class="pre">“mmTolerance=1”</span></code>. The <code class="docutils literal notranslate"><span class="pre">mmSubCell</span></code> keyword is
not used in point testing.</p>
</div>
<div class="section" id="example">
<h4>Example<a class="headerlink" href="#example" title="Permalink to this headline"></a></h4>
<p><a class="reference internal" href="#fig2-4a-5"><span class="std std-numref">Fig. 31</span></a> shows an example of a cask geometry with two types of
spent fuel (yellows), steel (blue), resin (green), and other metals
(gray). When the Denovo geometry is set up by testing only the center of
each mesh cell, the curved surfaces are not well represented (upper
right). By applying the ray-tracing method and defining a new material
made of partial fractions of the original materials, an improved Denovo
model can be made. In the lower left of the figure, the Denovo model was
constructed using one ray (in each dimension) per voxel and a tolerance
of 0.1. This gives 20 new materials that are a mixture of the original
13 actual materials and void. With <code class="docutils literal notranslate"><span class="pre">mmSubCells=3</span></code> and an <code class="docutils literal notranslate"><span class="pre">mmTolerance=0.01</span></code>,
139 macromaterials are created.</p>
<p>A macromaterial table listing the fractions of each macromaterial is
saved to a file called “<em>outputName</em>.mmt”, where <em>outputName</em> is the
name the user chose for his or her output file. This file can be used by
the Mesh File Viewer to display the macromaterials as mixtures of the
actual materials, as seen in lower row of <a class="reference internal" href="#fig2-4a-5"><span class="std std-numref">Fig. 31</span></a>. See the Mesh
File Viewer help pages for more information on how to use colormap files
and macromaterial tables.</p>
<div class="figure align-center" id="id10">
<span id="fig2-4a-5"></span><a class="reference internal image-reference" href="_images/fig51.png"><img alt="_images/fig51.png" src="_images/fig51.png" style="width: 600px;" /></a>
<p class="caption"><span class="caption-number">Fig. 31 </span><span class="caption-text">Cask geometry model (upper left) and the Denovo representation using (upper right) cell center testing. Representations using macromaterials determined by ray tracing are shown for (lower left) mmSubCell=1/mmTolerance=0.1 and (lower right) mmSubCell=3/mmTolerance=0.01.</span><a class="headerlink" href="#id10" title="Permalink to this image"></a></p>
</div>
</div>
</div>
<div class="section" id="starting-sources-block">
<h3>Starting sources block<a class="headerlink" href="#starting-sources-block" title="Permalink to this headline"></a></h3>
<p>The default KENO-VI starting source is “flat over the volume specified
by the unrotated, untranslated geometry record specified in the first
position of the global unit boundary record in fissile material only”.
For DEVC, the default starting source strength is uniform in the fissile
voxels contained within the bounding box of the global unit (uniform
density). If macromaterials are used, the amounts in each voxel are
volume averaged between fissile and non-fissile materials. <a class="reference internal" href="#tab2-4a-7"><span class="std std-numref">Table 30</span></a>
and <a class="reference internal" href="#tab2-4a-8"><span class="std std-numref">Table 31</span></a> describe the starting sources available in the DEVC
interface to Denovo.</p>
<span id="tab2-4a-7"></span><table class="docutils align-center" id="id11">
<caption><span class="caption-number">Table 30 </span><span class="caption-text">Starting source types (within the fissile areas of the listed shape)</span><a class="headerlink" href="#id11" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 33%" />
<col style="width: 33%" />
<col style="width: 33%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"></th>
<th class="head"><p>KENO-VI start type</p></th>
<th class="head"><p>DEVC</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>nst=0</p></td>
<td><p>the first surface of
boundary (default)</p></td>
<td><p>The bounding box of
global unit</p></td>
</tr>
<tr class="row-odd"><td><p>nst=0</p></td>
<td><p>Within boundary of
global array having a
reflector key set to
false</p></td>
<td><p>Not supported</p></td>
</tr>
<tr class="row-even"><td><p>nst=0</p></td>
<td><p>A cuboid defined by
XSM, XSP, YSM, YSP,
ZSM, and ZSP</p></td>
<td><p>Supported</p></td>
</tr>
<tr class="row-odd"><td><p>nst=1</p></td>
<td><p>A cuboid defined by
XSM, XSP, YSM, YSP,
ZSM, and ZSP with
cosine distributions</p></td>
<td><p>Supported</p></td>
</tr>
<tr class="row-even"><td><p>nst=2</p></td>
<td><p>Arbitrary fraction
(FCT) in element NXS,
NYS, NZS of the
global array with the
remainder in a cuboid
defined by XSM, XSP,
YSM, YSP, ZSM, and
ZSP with cosine
distributions</p></td>
<td><p>Supported for some
array types (see
<a class="reference internal" href="#tab2-4a-8"><span class="std std-numref">Table 31</span></a>)</p></td>
</tr>
<tr class="row-odd"><td><p>nst=3</p></td>
<td><p>At the location TFX,
TFY, TFZ in the
element NXS, NYS, NZS
of the global array</p></td>
<td><p>Supported for some
array types (see
<a class="reference internal" href="#tab2-4a-8"><span class="std std-numref">Table 31</span></a>)</p></td>
</tr>
<tr class="row-even"><td><p>nst=4</p></td>
<td><p>At the location TFX,
TFY, TFZ in units NBX
of the global array</p></td>
<td><p>Supported</p></td>
</tr>
<tr class="row-odd"><td><p>nst=5</p></td>
<td><p>Across units NBX in
the global array</p></td>
<td><p>Not supported</p></td>
</tr>
<tr class="row-even"><td><p>nst=6</p></td>
<td><p>List of points TFX,
TFY, TFZ in global
coordinates</p></td>
<td><p>Limited to 1 point</p></td>
</tr>
<tr class="row-odd"><td><p>nst=6</p></td>
<td><p>List of points TFX,
TFY, TFZ in element
NXS, NYS, NZS of the
global array</p></td>
<td><p>Limited to 1 point
and only for some
array types (see
<a class="reference internal" href="#tab2-4a-8"><span class="std std-numref">Table 31</span></a>)</p></td>
</tr>
<tr class="row-even"><td><p>nst=7</p></td>
<td><p>Flat distributions in
X and Y with
[1-cos<sup>2</sup>(z)]
in Z for a cuboid
defined by XSM, XSP,
YSM, YSP, ZSM, and
ZSP</p></td>
<td><p>Supported</p></td>
</tr>
<tr class="row-odd"><td><p>nst=8</p></td>
<td><p>Flat distributions in
X and Y with a
segmented
distribution in Z for
a cuboid defined by
XSM, XSP, YSM, YSP,
ZSM, and ZSP</p></td>
<td><p>Not supported</p></td>
</tr>
<tr class="row-even"><td><p>nst=9</p></td>
<td><p>Use a mesh source
lite file</p></td>
<td><p>Not supported</p></td>
</tr>
</tbody>
</table>
<span id="tab2-4a-8"></span><table class="docutils align-center" id="id12">
<caption><span class="caption-number">Table 31 </span><span class="caption-text">Supported array types for starting sources</span><a class="headerlink" href="#id12" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 56%" />
<col style="width: 44%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>no arrays</p></th>
<th class="head"><p>supported</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>cuboid</p></td>
<td><p>supported</p></td>
</tr>
<tr class="row-odd"><td><p>hexagonal</p></td>
<td><p>supported</p></td>
</tr>
<tr class="row-even"><td><p>shexagonal</p></td>
<td><p>no</p></td>
</tr>
<tr class="row-odd"><td><p>rhexagonal</p></td>
<td><p>no</p></td>
</tr>
<tr class="row-even"><td><p>dodecahedral</p></td>
<td><p>no</p></td>
</tr>
</tbody>
</table>
<p>The starting source initialized in Denovo is always a volumetric source—DEVC does not create point sources (which would activate the first
collision option in Denovo).</p>
</div>
</div>
<div class="section" id="sequence-output">
<h2>Sequence Output<a class="headerlink" href="#sequence-output" title="Permalink to this headline"></a></h2>
<p>The main text output file consists of the output from the cross-section
processing codes and Denovo. The user should examine the output and pay
attention to any warnings or errors. <a class="reference internal" href="#tab2-4a-9"><span class="std std-numref">Table 32</span></a> lists the files
generated during the DEVC sequence.</p>
<span id="tab2-4a-9"></span><table class="docutils align-center" id="id13">
<caption><span class="caption-number">Table 32 </span><span class="caption-text">Files created by DEVC for an input file named <em>input</em>.inp</span><a class="headerlink" href="#id13" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p><strong>Filename</strong></p></th>
<th class="head"></th>
<th class="head"><p><strong>Viewer</strong></p></th>
<th class="head"><p><strong>Description</strong></p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>Output Summary</p></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td><p><em>input</em>.out</p></td>
<td></td>
<td><p>main text
output file,
contains
<span class="math notranslate nohighlight">\(k_{\math
rm{\text{eff}}}\)</span></p></td>
</tr>
<tr class="row-even"><td></td>
<td><p><em>input</em>.msg</p></td>
<td></td>
<td><p>messages file</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p>Denovo</p></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>xkba_b.inp</p></td>
<td><p>V<sup>a</sup></p></td>
<td><p>input file for
Denovo – if
this file is
renamed to have</p>
<p>a *.dsi
extension
(Denovo simple
input), it is
viewable</p>
<p>in the Mesh
File Viewer</p>
</td>
</tr>
<tr class="row-even"><td></td>
<td><p>ft02f001</p></td>
<td></td>
<td><p>AMPX formatted
cross sections
for Denovo</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p><em>input</em>.mmt</p></td>
<td><p>V</p></td>
<td><p>macromaterial
table, use with
*.dso or
*.dsi file</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td><p><em>input</em>.dff</p></td>
<td><p>V</p></td>
<td><p>Denovo fission
fluxes</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p><em>input</em>.dso</p></td>
<td><p>V</p></td>
<td><p>Denovo fission
source
distribution</p></td>
</tr>
<tr class="row-odd"><td><p><sup>a</sup>V – can be displayed
with the Mesh File Viewer.</p></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<div class="section" id="using-the-mesh-file-viewer">
<h3>Using the mesh file viewer<a class="headerlink" href="#using-the-mesh-file-viewer" title="Permalink to this headline"></a></h3>
<p>The Mesh File Viewer is a Java utility shipped with SCALE that is used
for viewing mesh tallies from Monaco, as well as importance maps and
mesh-based sources in MAVRIC. The Mesh File Viewer can be used with DEVC
to view the Denovo input file (*.dsi, showing the starting source), the
Denovo output fission source distribution (*.dso) file, or the Denovo
output flux (*.dff) file.</p>
<p>With any Denovo file, material information for each voxel can be
displayed. Users can use the graphical user interface to select colors
for each material in the DEVC input and save them to a colormap text
file (*.cmp) for later use. For example, <a class="reference internal" href="#fig2-4a-6"><span class="std std-numref">Fig. 32</span></a> shows a cask
model that has 13 materials with the default colors assigned by the
viewer. A better color map (uranium is yellow, steel is blue, etc.) and
an image using that color map are also shown in <a class="reference internal" href="#fig2-4a-6"><span class="std std-numref">Fig. 32</span></a>.</p>
<div class="figure align-center" id="id14">
<span id="fig2-4a-6"></span><a class="reference internal image-reference" href="_images/fig6.png"><img alt="_images/fig6.png" src="_images/fig6.png" style="width: 500px;" /></a>
<p class="caption"><span class="caption-number">Fig. 32 </span><span class="caption-text">Viewing material information with the Mesh File Viewer.</span><a class="headerlink" href="#id14" title="Permalink to this image"></a></p>
</div>
<p>If the Denovo input was made using the mixed macromaterials, that can
also be shown with the Mesh File Viewer. When one of the mesh files is
loaded and the geometry is displayed (e.g., the materials for a cask
model shown in <a class="reference internal" href="#fig2-4a-7"><span class="std std-numref">Fig. 33</span></a>), there will be many values since each
macromaterial is treated by the Java viewer as a separate material.
Redefining the color map using the GUI is not realistic.</p>
<p>A colormap needs to be defined for the original materials of the
problem. For this example, there are 13 original materials, but when
using macromaterials, 73 macromaterials are used in the
discrete-ordinates model (as listed in the *.mmt file). The colormap
file should only contain values for the 13 original materials. When
loading the colormap, a corresponding *.mmt file can also be loaded.
This will display mixed colors for the macromaterials, as shown in
<a class="reference internal" href="#fig2-4a-7"><span class="std std-numref">Fig. 33</span></a>.</p>
<p>The final result is an image where the colors for the different values
of the geometry attribute (which in the above example is material) are
mixed in the ratio of the macromaterial definition.</p>
<div class="figure align-center" id="id15">
<span id="fig2-4a-7"></span><a class="reference internal image-reference" href="_images/fig7.png"><img alt="_images/fig7.png" src="_images/fig7.png" style="width: 500px;" /></a>
<p class="caption"><span class="caption-number">Fig. 33 </span><span class="caption-text">Viewing material information from a Denovo input file.</span><a class="headerlink" href="#id15" title="Permalink to this image"></a></p>
</div>
</div>
<div class="section" id="viewing-the-starting-source">
<h3>Viewing the starting source<a class="headerlink" href="#viewing-the-starting-source" title="Permalink to this headline"></a></h3>
<p>The Java MeshFileViewer (scale/cmds/meshview) can be used to visualize
the Denovo binary stream input file to show materials and starting
source strengths. An example is shown in <a class="reference internal" href="#fig2-4a-8"><span class="std std-numref">Fig. 34</span></a>.</p>
<p><strong>Material Numbering</strong></p>
<p>The cross sections produced by the SCALE cross-section mixing module ICE
typically have a number of materials equal to the maximum material ID
specified by the user in the “read composition” block. For a user input
that contains materials 1, 3, and 5, the GIP-formatted cross-section
file will contain five entries. For each lattice cell calculation that
uses a cellmix= parameter, one more entry is contained in the GIP file.
Hence, the GIP file does not contain the user’s value from the
“cellmix=” parameter but instead numbers the cellmix materials
sequentially starting from 1+maximum(material ID). The Denovo geometry
input and macroMixTable file produced by DEVC are modified to match the
GIP cross-section file. When viewing the Denovo binary input file with
the Mesh File Viewer, the GIP numbering for materials will be seen.</p>
<div class="figure align-center" id="id16">
<span id="fig2-4a-8"></span><a class="reference internal image-reference" href="_images/fig8.png"><img alt="_images/fig8.png" src="_images/fig8.png" style="width: 500px;" /></a>
<p class="caption"><span class="caption-number">Fig. 34 </span><span class="caption-text">Fine-mesh version of sample problem 8, showing the materials using macromaterial blending of UO<sub>2</sub>, MOX, clad, and water (left) and the starting source strength limited to cells with fissionable material (right).</span><a class="headerlink" href="#id16" title="Permalink to this image"></a></p>
</div>
</div>
</div>
<div class="section" id="sample-problems">
<h2>Sample Problems<a class="headerlink" href="#sample-problems" title="Permalink to this headline"></a></h2>
<p>Sample problems have been made that correspond to the eight CSAS6 sample
problems. In each problem, the KENO parameters block was commented out,
a parameters block containing Denovo calculation parameters was added,
and a grid geometry block was added. These sample problems use a coarse
discretization and loose tolerances to obtain a short runtime. Users
will typically use much finer discretization (mesh, quadrature) and
higher fidelity parameter settings for real eigenvalue calculations. The
voxelized geometry and starting source distribution are shown below in
<a class="reference internal" href="#fig2-4a-9"><span class="std std-numref">Fig. 35</span></a>.</p>
<p>Results for the sample problems are displayed in <a class="reference internal" href="#tab2-4a-10"><span class="std std-numref">Table 33</span></a>. The
sample problems used QR 1/1, a P<sub>0</sub> scattering expansion, a k
tolerance of 0.001 and coarse meshes for speed. The higher fidelity runs
used finer spatial meshes, default parameters of QR 2/2, <em>P</em><sub>0</sub>
scattering expansion, and the default <em>k</em> tolerance (10:sup:<cite>-5</cite>).
Results for the longer-time CSAS6 and higher fidelity Denovo
calculations are shown in <a class="reference internal" href="#fig2-4a-10"><span class="std std-numref">Fig. 36</span></a>.</p>
<div class="figure align-center" id="id17">
<span id="fig2-4a-9"></span><a class="reference internal image-reference" href="_images/fig9.png"><img alt="_images/fig9.png" src="_images/fig9.png" style="width: 600px;" /></a>
<p class="caption"><span class="caption-number">Fig. 35 </span><span class="caption-text">Denovo geometry (left) and starting source distribution (right) for the sample problems.</span><a class="headerlink" href="#id17" title="Permalink to this image"></a></p>
</div>
<div class="figure align-center" id="id18">
<span id="fig2-4a-10"></span><a class="reference internal image-reference" href="_images/fig10.png"><img alt="_images/fig10.png" src="_images/fig10.png" style="width: 500px;" /></a>
<p class="caption"><span class="caption-number">Fig. 36 </span><span class="caption-text">Fission source distributions computed by CSAS6 (left) and Denovo (right).</span><a class="headerlink" href="#id18" title="Permalink to this image"></a></p>
</div>
<table class="docutils align-center" id="tab2-4a-10">
<caption><span class="caption-number">Table 33 </span><span class="caption-text">Sample problem results</span><a class="headerlink" href="#tab2-4a-10" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 100%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><img alt="_images/tab10.png" src="_images/tab10.png" />
</td>
</tr>
</tbody>
</table>
<p id="bibtex-bibliography-DEVC-0"><dl class="citation">
<dt class="bibtex label" id="evans-denovo-2010"><span class="brackets"><a class="fn-backref" href="#id1">ESSC10</a></span></dt>
<dd><p>Thomas M. Evans, Alissa S. Stafford, Rachel N. Slaybaugh, and Kevin T. Clarno. Denovo: A new three-dimensional parallel discrete ordinates code in SCALE. <em>Nuclear technology</em>, 171(2):171–200, 2010. Publisher: Taylor &amp; Francis.</p>
</dd>
<dt class="bibtex label" id="goluoglu-monte-2011"><span class="brackets"><a class="fn-backref" href="#id2">GPJD+11</a></span></dt>
<dd><p>Sedat Goluoglu, Lester M. Petrie Jr, Michael E. Dunn, Daniel F. Hollenbach, and Bradley T. Rearden. Monte Carlo criticality methods and analysis capabilities in SCALE. <em>Nuclear Technology</em>, 174(2):214–235, 2011. Publisher: Taylor &amp; Francis.</p>
</dd>
<dt class="bibtex label" id="ibrahim-improving-2009"><span class="brackets"><a class="fn-backref" href="#id3">IPE+09</a></span></dt>
<dd><p>Ahmad M. Ibrahim, Douglas E. Peplow, Thomas M. Evans, John C. Wagner, and Paul PH Wilson. Improving the Mesh Generation Capabilities in the SCALE Hybrid Shielding Analysis Sequence. <em>Trans. Am. Nucl. Soc</em>, 100:302, 2009.</p>
</dd>
<dt class="bibtex label" id="johnson-fast-2013"><span class="brackets"><a class="fn-backref" href="#id4">Joh13</a></span></dt>
<dd><p>Seth R. Johnson. Fast mix table construction for material discretization. In <em>Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering-M and C 2013</em>. 2013.</p>
</dd>
</dl>
</p>
</div>
</div>


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