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<p class="caption"><span class="caption-text">Reactor Physics</span></p>
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="Polaris.html">Polaris: 2D Light Water Reactor Lattice Physics Module</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">SCALE 6.3 Polaris Input Format</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#box-version-6-3-channel-box-geometry">box (Version 6.3) – channel box geometry</a></li>
<li class="toctree-l2"><a class="reference internal" href="#pin-version-6-3-pincell-comprised-of-nested-geometry-zones-of-variable-shape">pin (Version 6.3) – pincell comprised of nested geometry zones of variable shape</a></li>
<li class="toctree-l2"><a class="reference internal" href="#mesh-version-6-3-advanced-material-dependent-meshing-options">mesh (Version 6.3) – advanced material dependent meshing options</a></li>
<li class="toctree-l2"><a class="reference internal" href="#cross-version-6-3-cross-geometry">cross (Version 6.3) – cross geometry</a></li>
<li class="toctree-l2"><a class="reference internal" href="#dxmap-and-dymap-version-6-3-pin-by-pin-displacement-maps">dxmap and dymap (Version 6.3) – pin-by-pin displacement maps</a></li>
<li class="toctree-l2"><a class="reference internal" href="#control-blade-version-6-3-bwr-control-blade">control&lt;BLADE&gt; (Version 6.3) – BWR control blade</a></li>
<li class="toctree-l2"><a class="reference internal" href="#option-geom-version-6-3-geometry-options">option&lt;GEOM&gt; (Version 6.3) – geometry options</a></li>
<li class="toctree-l2"><a class="reference internal" href="#bu-version-6-3-initiate-calculation-with-cumulative-burnups">bu (Version 6.3) – initiate calculation with cumulative burnups</a></li>
<li class="toctree-l2"><a class="reference internal" href="#bui-version-6-3-initiate-calculation-with-cumulative-burnups-with-restart">bui (Version 6.3) – initiate calculation with cumulative burnups (with restart)</a></li>
<li class="toctree-l2"><a class="reference internal" href="#dbu-version-6-3-initiate-calculation-with-incremental-burnups">dbu (Version 6.3) – initiate calculation with incremental burnups</a></li>
<li class="toctree-l2"><a class="reference internal" href="#t-version-6-3-initiate-calculation-by-cumulative-time">t (Version 6.3) – initiate calculation by cumulative time</a></li>
<li class="toctree-l2"><a class="reference internal" href="#ti-version-6-3-initiate-calculation-by-cumulative-time-with-restart">ti (Version 6.3) – initiate calculation by cumulative time (with restart)</a></li>
<li class="toctree-l2"><a class="reference internal" href="#dt-version-6-3-initiate-calculation-by-incremental-time">dt (Version 6.3) – initiate calculation by incremental time</a></li>
<li class="toctree-l2"><a class="reference internal" href="#state-version-6-3-property-state-specification">state (Version 6.3) – property state specification</a></li>
<li class="toctree-l2"><a class="reference internal" href="#history-version-6-3-time-dependent-history">history (Version 6.3) – time-dependent history</a></li>
<li class="toctree-l2"><a class="reference internal" href="#option-gamma-version-6-3-gamma-transport-calculation">option&lt;GAMMA&gt; (Version 6.3) – gamma transport calculation</a></li>
<li class="toctree-l2"><a class="reference internal" href="#detector-version-6-3-insert-a-detector-geometry">detector (Version 6.3) – insert a detector geometry</a></li>
<li class="toctree-l2"><a class="reference internal" href="#option-essm-modified-in-version-6-3-embedded-self-shielding">option&lt;ESSM&gt; (modified in Version 6.3) – embedded self-shielding</a></li>
<li class="toctree-l2"><a class="reference internal" href="#option-fg-modified-in-version-6-3-few-group-cross-section-generation">option&lt;FG&gt; (modified in Version 6.3) – few-group cross section generation</a></li>
<li class="toctree-l2"><a class="reference internal" href="#property-grain-version-6-3-grain-property-used-to-model-stochastic-media">property&lt;GRAIN&gt; (Version 6.3) – grain property used to model stochastic media</a></li>
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<p class="caption"><span class="caption-text">Criticality Safety</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Criticality%20Safety%20Overview.html">Criticality Safety Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="CSAS5.html">CSAS5: Control Module For Enhanced Criticality Safety Analysis Sequences With KENO V.a</a></li>
<li class="toctree-l1"><a class="reference internal" href="CSAS5App.html">Additional Example Applications of CSAS5</a></li>
<li class="toctree-l1"><a class="reference internal" href="CSAS6.html">CSAS6: Control Module for Enhanced Criticality Safety Analysis with KENO-VI</a></li>
<li class="toctree-l1"><a class="reference internal" href="CSAS6App.html">Additional Example Applications of CSAS6</a></li>
<li class="toctree-l1"><a class="reference internal" href="STARBUCS.html">STARBUCS: A Scale Control Module for Automated Criticality Safety Analyses Using Burnup Credit</a></li>
<li class="toctree-l1"><a class="reference internal" href="Sourcerer.html">Sourcerer: Deterministic Starting Source for Criticality Calculations</a></li>
<li class="toctree-l1"><a class="reference internal" href="DEVC.html">DEVC: Denovo EigenValue Calculation</a></li>
<li class="toctree-l1"><a class="reference internal" href="KMART.html">KMART5 and KMART6: Postprocessors for KENO V.A and KENO-VI</a></li>
<li class="toctree-l1"><a class="reference internal" href="K5C5.html">K5toK6 and C5toC6: Input File Conversion Programs for KENO and CSAS</a></li>
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<p class="caption"><span class="caption-text">Material Specification and Cross Section Processing</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Material%20Specification%20and%20Cross%20Section%20Processing%20Overview.html">Material Specification and Cross Section Processing Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="XSProc.html">XSPROC: The Material and Cross Section Processing Module for SCALE</a></li>
<li class="toctree-l1"><a class="reference internal" href="XSProcAppA.html">XSProc: Standard Composition Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="XSProcAppB.html">XSProc Standard Composition Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="XSProcAppC.html">Examples of Complete XSProc Input Data</a></li>
<li class="toctree-l1"><a class="reference internal" href="stdcmp.html">Standard Composition Library</a></li>
<li class="toctree-l1"><a class="reference internal" href="BONAMI.html">BONAMI: Resonance Self-Shielding by the Bondarenko Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="CENTRM.html">CENTRM: A Neutron Transport Code for Computing Continuous-Energy Spectra in General One-Dimensional Geometries and Two-Dimensional Lattice Cells</a></li>
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<p class="caption"><span class="caption-text">Monte Carlo Transport</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="Monte%20Carlo%20Transport%20Overview.html">Monte Carlo Transport Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="Keno.html">Keno: A Monte Carlo Criticality Program</a></li>
<li class="toctree-l1"><a class="reference internal" href="KenoA.html">Keno Appendix A: KENO V.a Shape Descriptions</a></li>
<li class="toctree-l1"><a class="reference internal" href="KenoB.html">Keno Appendix B: KENO VI Shape Descriptions</a></li>
<li class="toctree-l1"><a class="reference internal" href="KenoC.html">Keno Appendix C: Sample problems</a></li>
<li class="toctree-l1"><a class="reference internal" href="Monaco.html">Monaco: A Fixed-Source Monte Carlo Transport Code for Shielding Applications</a></li>
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<p class="caption"><span class="caption-text">Radiation Shielding</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="MAVRIC.html">MAVRIC: Monaco with Automated Variance Reduction using Importance Calculations</a></li>
<li class="toctree-l1"><a class="reference internal" href="CAAScapability.html">MAVRIC Appendix A: CAAS Capability</a></li>
<li class="toctree-l1"><a class="reference internal" href="appendixb.html">MAVRIC Appendix B: MAVRIC Utilities</a></li>
<li class="toctree-l1"><a class="reference internal" href="appendixc.html">MAVRIC Appendix C: Advanced Features</a></li>
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<div class="section" id="scale-6-3-polaris-input-format">
<span id="a"></span><h1>SCALE 6.3 Polaris Input Format<a class="headerlink" href="#scale-6-3-polaris-input-format" title="Permalink to this headline"></a></h1>
<p>For the release of SCALE 6.2.3, several new input cards were implemented
into Polaris to model boiling water reactor (BWR) geometries and
neutron/gamma detectors, which requires a gamma transport calculation.
Moreover, improvements to existing input cards were implemented, along
with the ability to specify time-dependent state properties and the
ability to specify one or more depletion histories. This appendix
describes the new and modified input cards that will be included in the
Polaris input format for SCALE 6.3, which are accessible as part of the
release of SCALE 6.2.3.</p>
<p>To maximize backwards compatibility for input files developed with the
original SCALE 6.2.0 release, the new and modified input cards are not
available <em>by default</em> with SCALE 6.2.3. The new and modified input
cards are activated if the input file begins with =polaris_6.3 rather
than =polaris. The suffix “_6.3” is an indicator to the Polaris input
processor to use the SCALE 6.3 input format. For the future release of
SCALE 6.3, the original input cards supported in the SCALE 6.2 input
format will be available if the input file begins with =polaris_6.2.</p>
<p>The new input cards to model BWR geometries include:</p>
<ul class="simple">
<li><p><strong>cross</strong> – define the interior water cross geometry of SVEA assembly
designs;</p></li>
<li><p><strong>dxmap</strong> (or <strong>dymap</strong>) – define displacement maps that indicate
that translation of the pin center in the x- (or y-) direction;</p></li>
<li><p><strong>control &lt;BLADE&gt;</strong> - define the control blade geometry;</p></li>
<li><p><strong>mesh</strong> – define advanced spatial meshing options for different
materials; and</p></li>
<li><p><strong>option &lt;GEOM&gt;</strong> – define geometry tolerances, advance meshing
options, and plotting options.</p></li>
</ul>
<p>The modified input cards to model BWR geometries include:</p>
<ul class="simple">
<li><p><strong>pin</strong> – define circular and square-based geometry zones, as well as
arbitrarily sized pins, e.g. size=1.5 water rod in some 9x9 BWR
lattice designs; and</p></li>
<li><p><strong>box</strong> – define channel box geometry with arbitrary number of zones
and cutout regions.</p></li>
</ul>
<p>For neutron/gamma detector modeling, there is a new <strong>detector</strong> card
and an addition to the existing <strong>option &lt;FG&gt;</strong> card to enable output to
the few-group cross section output (T16) file.</p>
<p>To control the gamma calculation, an <strong>option &lt;GAMMA&gt;</strong> has been added.</p>
<p>The new input cards for time-dependent modeling include:</p>
<ul class="simple">
<li><p><strong>history</strong> – define one or more operating histories in the input
file; and</p></li>
<li><p><strong>bui</strong> (or <strong>ti</strong>) – define restart cumulative burnup (or time)
values.</p></li>
</ul>
<p>The modified input cards for time-dependent modeling include:</p>
<ul class="simple">
<li><p><strong>state</strong> – define one or more time-independent or time-dependent
state properties;</p></li>
<li><p><strong>bu</strong> (or <strong>t</strong>) – define cumulative burnup (or time) values; and</p></li>
<li><p><strong>dbu</strong> (or <strong>dt</strong>) – define incremental burnup (or time) values.</p></li>
</ul>
<p>Example input files are included in the ${SCALE}/regression/input
directory:</p>
<ul class="simple">
<li><p>polaris.6.3.atrium9x9.inp and polaris.6.3.atrium10x10.inp –
prototypic ATRIUM models;</p></li>
<li><p>polaris.6.3.blade1.inp and polaris.6.3.blade2.inp – control &lt;BLADE&gt;
examples;</p></li>
<li><p>polaris.6.3.ge7x7.inp through polaris.6.3.ge10x10.inp – prototypic GE
models;</p></li>
<li><p>polaris.6.3.svea100.inp and polaris.6.3.svea64.inp – prototypic SVEA
models; and</p></li>
<li><p>polarisHistory.inp: history example.</p></li>
</ul>
<div class="section" id="box-version-6-3-channel-box-geometry">
<span id="a-1"></span><h2>box (Version 6.3) – channel box geometry<a class="headerlink" href="#box-version-6-3-channel-box-geometry" title="Permalink to this headline"></a></h2>
<p><strong>box</strong> thick=<em>Real</em> [rad=*Real*] [hspan=*Real*] [Mbox=MNAME]
[cothick=*Real*] [cobtm=*Real*] [cotop=*Real*]</p>
<blockquote>
<div><div class="line-block">
<div class="line">[: t<sub>2</sub> t<sub>3</sub> … t<sub>i</sub> … t<sub>N</sub></div>
<div class="line">[: a<sub>2</sub> a<sub>3</sub> … a<sub>i</sub> … a<sub>N</sub></div>
<div class="line">[: b<sub>2</sub> b<sub>3</sub> … b<sub>i</sub> … b<sub>N</sub></div>
<div class="line">[: M<sub>2</sub> M<sub>3</sub> … M<sub>i</sub> … M<sub>N</sub></div>
<div class="line">[: r<sub>2</sub> r<sub>3</sub> … r<sub>i</sub> … r<sub>N+1</sub> ]]]]]</div>
</div>
</div></blockquote>
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<p>Examples:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>% simple
box 0.2
% rounded corner, rad 0.9
box 0.2 0.9
% rounded corner and user-defined inner span
box 0.2 0.9 6.7
% two zones
box 0.2 0.9 6.7
: 0.2
: 4.0
: 4.3
</pre></div>
</div>
<p>Comments:</p>
<p>The <strong>box</strong> specifies the channel box geometry that surrounds the
<strong>pinmap</strong>. The three primary dimensions of the channel box are the
thickness (thick), the inner corner radius (rad), and the half inner
span (hspan). Several additional dimensions for both <strong>box</strong> and
<strong>cross</strong> are defined with respect to the channel box center. The
channel box center is not to be confused with the lattice center: the
former is the centroid of the inner channel box square boundary and the
latter will depend on the wide and narrow gap dimensions provided on the
<strong>hgap</strong> card. By default, the half inner span is equal to the half pin
pitch multiplied by the number of pins on each side of the assembly (see
npins and ppitch on the <strong>geometry&lt;ASSM&gt;</strong> card). If a <strong>cross</strong> card is
applied, the default half inner span is increased by the half width of
the interior cross buffer region (see hwidth on the <strong>cross</strong> card).</p>
<p>Additional channel box zones can be specified on the <strong>box</strong> card. The
additional zones are useful for defining thick corner regions of the
channel box. Each additional zone must have a user-defined thickness
(t:sub:<cite>i</cite>, i = 2 to N). Note that the starting index begins at “2”
rather than “1” because the zone 1 thickness has already been defined by
the “thick” input field.</p>
<p>“Cutout regions” may be defined in which a portion of the channel box
zone is replaced by the corresponding <strong>hgap</strong> material along the
horizontal and vertical centerlines of the channel box. The cutout
region is defined by the distance from the channel box centerline to the
bottom additional channel box zone (a:sub:<cite>i</cite>) and the top of the
channel box zone (b:sub:<cite>i</cite>). The values of a<sub>i</sub> and b<sub>i</sub>
determine the size of trapezoidal cutout region centered along each face
of the channel box. The b<sub>i</sub> value must be greater than or equal
to the a<sub>i</sub> value. The a<sub>i</sub> value must be greater than or
equal to the previous zone’s b<sub>i</sub> value, i.e., b<sub>i-1</sub>. By
default, a<sub>2</sub> and b<sub>2</sub> are zero. If only M cutout regions
are specified for N additional zones, i.e., M &lt; N, both a<sub>i</sub> and
b<sub>i</sub> is set to b<sub>M</sub> for i = M+1 to N.</p>
<p>Additional zones can also have a different inner corner radius
(r:sub:<cite>2</cite> … r<sub>N</sub>). The outer corner radius of the last zone may
also be specified (r:sub:<cite>N+1</cite>). By default, r<sub>2</sub> is zero if rad
is zero. If rad is greater than zero, the default value of r<sub>2</sub>
is rad+thick. Similar rules apply for determining the default corner
radii for additional zones if they are omitted in the input
specification.</p>
<p>Additional zones can also have a different material (M:sub:<cite>i</cite>). By
default, M<sub>2</sub> is M<sub>box</sub>. If additional materials are
omitted in the input, the default value of M<sub>i</sub> is M<sub>i-1</sub>
for i = 3 to N.</p>
<p>The spatial mesh along each face of the channel box will be determined
by the nf values specified on the hgap card.</p>
<p>The four examples listed above are displayed in <a class="reference internal" href="#fig3-2a-1"><span class="std std-numref">Fig. 5</span></a>. For
additional examples, see the polaris.6.3 regression input files
described at the beginning of <a class="reference internal" href="#a"><span class="std std-ref">SCALE 6.3 Polaris Input Format</span></a>.</p>
<p>See also:</p>
<p><strong>geometry&lt;ASSM&gt;, hgap, cross (Version 6.3)</strong></p>
<div class="figure align-center" id="id7">
<span id="fig3-2a-1"></span><a class="reference internal image-reference" href="_images/fig1103.png"><img alt="_images/fig1103.png" src="_images/fig1103.png" style="width: 400px;" /></a>
<p class="caption"><span class="caption-number">Fig. 5 </span><span class="caption-text">Box card examples.</span><a class="headerlink" href="#id7" title="Permalink to this image"></a></p>
</div>
</div>
<div class="section" id="pin-version-6-3-pincell-comprised-of-nested-geometry-zones-of-variable-shape">
<span id="a-2"></span><h2>pin (Version 6.3) – pincell comprised of nested geometry zones of variable shape<a class="headerlink" href="#pin-version-6-3-pincell-comprised-of-nested-geometry-zones-of-variable-shape" title="Permalink to this headline"></a></h2>
<div class="line-block">
<div class="line"><strong>pin</strong> PINID [size=*Real*]
| : r<sub>1</sub> r<sub>2</sub> … r<sub>i</sub> … r<sub>N</sub>
| : M<sub>1</sub> M<sub>2</sub> … M<sub>i</sub> … M<sub>N</sub> [M<sub>out</sub>]
| [: S<sub>1</sub> S<sub>2</sub> … S<sub>i</sub> … S<sub>N</sub>]</div>
</div>
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</td>
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</table>
<p>Examples:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>%standard fuel pin
pin 1 : 0.4096 0.418 0.475 : FUEL.1 GAP.1 CLAD.1
%2x2 water rod
pin W 2.0 : 1.6 1.7 : MOD.1 TUBE.1
%3x3 square water box (ATRIUM)
pin W 3.0 : 1.68 1.75 : MOD.1 TUBE.1 : SQR SQR
%noninteger size water rod (GE9x9)
pin W 1.76 : 1.16 1.259 : MOD.1 TUBE.1 COOL.2
</pre></div>
</div>
<p>Comments:</p>
<p>The <strong>pin</strong> card is one of the basic building blocks of the assembly
model. <strong>pin</strong> and <strong>slab</strong> are the only geometry components which
allows an integer (<em>Int</em>) identifier as well as a <em>Word</em>—all other
geometric identifiers use <em>Word</em>. Note that the materials are required,
except for the last M<sub>out</sub>, which can be used to overwrite the
material given by a <strong>channel</strong> for the outermost region in the pincell.
The <strong>pin</strong> geometry is constructed from the inside out, using either
circle zones (defined by the radius) or square zones (defined by the
half-width, and optional corner radius). Different examples of pin
geometries are displayed in <a class="reference internal" href="#fig3-2a-2"><span class="std std-numref">Fig. 6</span></a>. All meshing options for the
<strong>pin</strong> are provided through the <strong>mesh</strong> card.</p>
<p>If the pin size is an integer value, the pin consumes a size×size
subarray in the <strong>pinmap</strong> (e.g. 1×1, 2×2, 3×3, etc). If the pin size is
noninteger, the pin consumes a <em>ceil</em>(size)×*ceil*(size) subarray in
the <strong>pinmap</strong>. <em>ceil(x)</em> represents the ceiling function to round the
value of x to the nearest integer greater than or equal to x. For size
equal to 1.3, each instance of the pin will consume a 2×2 subarray in
the <strong>pinmap</strong>. Each instance of a noninteger-sized pin must share a
location with another instance of a noninteger-sized pin, but not
necessarily the same pin. The shared location must be set to “_” in the
<strong>pinmap</strong>. The identification of the shared location is necessary to
determine the center of each pin. The pin center is at a distance of
size*half pitch*sqrt(2) from the opposite corner of the shared location,
along the diagonal of the pin boundary. An example of an integer-sized
pins is displayed in <a class="reference internal" href="#fig3-2a-2"><span class="std std-numref">Fig. 6</span></a>. An example of noninteger-sized pins
is displayed in <a class="reference internal" href="#fig3-2a-3"><span class="std std-numref">Fig. 7</span></a>.</p>
<div class="figure align-center" id="id8">
<span id="fig3-2a-2"></span><a class="reference internal image-reference" href="_images/fig215.png"><img alt="_images/fig215.png" src="_images/fig215.png" style="width: 400px;" /></a>
<p class="caption"><span class="caption-number">Fig. 6 </span><span class="caption-text">Pin examples with different shape geometries.</span><a class="headerlink" href="#id8" title="Permalink to this image"></a></p>
</div>
<div class="figure align-center" id="id9">
<span id="fig3-2a-3"></span><a class="reference internal image-reference" href="_images/fig314.png"><img alt="_images/fig314.png" src="_images/fig314.png" style="width: 400px;" /></a>
<p class="caption"><span class="caption-number">Fig. 7 </span><span class="caption-text">Pin examples with noninteger pin size.</span><a class="headerlink" href="#id9" title="Permalink to this image"></a></p>
</div>
<p>For additional examples, see the polaris.6.3 regression input files
described at the beginning of this section.</p>
<p>See also:</p>
<p><strong>slab, pinmap</strong>, <strong>channel, mesh (Version 6.3)</strong></p>
</div>
<div class="section" id="mesh-version-6-3-advanced-material-dependent-meshing-options">
<span id="a-3"></span><h2>mesh (Version 6.3) – advanced material dependent meshing options<a class="headerlink" href="#mesh-version-6-3-advanced-material-dependent-meshing-options" title="Permalink to this headline"></a></h2>
<div class="line-block">
<div class="line"><strong>mesh</strong> MSPEC : [m=*Real*] [nx=*Int*] [ny=*Int*] [mx=*Real*]
[my=*Real*]
| [nr=*Int*] [ns=*Int*] [mr=*Real*] [ms=*Real*]
| [nf=*Int*] [nd=*Int*] [mf=*Real*] [md=*Real*]</div>
</div>
<table class="docutils align-center">
<colgroup>
<col style="width: 100%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><a class="reference internal image-reference" href="_images/3-2a-3-tab.svg"><img alt="_images/3-2a-3-tab.svg" class="align-center" src="_images/3-2a-3-tab.svg" width="800" /></a>
</td>
</tr>
</tbody>
</table>
<p>Examples:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>mesh COOL : nr=3 ns=4 nx=2 ny=2 %coolant mesh: 3 ring, 4 sectors, 2 in x and y
mesh MOD.1 : nf=2 nd=4 %mesh used for wide gap (MOD.1): nf=2 nd=4
mesh MOD.2 : nf=2 nd=3 %mesh used for narrow gap (MOD.2): nf=2 nd=3
mesh FUEL : mr=2.0 %double the fuel radial mesh
mesh FUEL.2 : m=3.0 %triple all mesh values for FUEL.2
mesh CLAD : ms=0.5 %coarsen the clad sector mesh by a factor of 1/2.
</pre></div>
</div>
<p>Comments:</p>
<p>Polaris supports three different mesh types: 1) cylindrical mesh for CIR
shapes in the pin card, 2) Cartesian mesh for SQR shapes in the pin
card, and 3) a special Cartesian mesh for the region external to the
pinmap region. As shown in the examples above, the mesh card is used to
define, refine, or coarsen the mesh parameters for one or more of the
mesh types associated with a given material class or material name. The
default values for mesh parameters are defined through the option&lt;GEOM&gt;
card and the system card. The default values on the option&lt;GEOM&gt; card
are nr=1, ns=1, nx=1, ny=1, nf=1, nd=1, and MeshMult=1.0. The “MeshMult”
multiplier from the option&lt;GEOM&gt; is a global mesh multiplier applied in
conjunction with any material-specific multiplier (see option&lt;GEOM&gt;
example for details). If system BWR or system PWR is applied, new
default values include nf=2, ns=8, and nr=2 (only for the channel
material class). If the final mesh value is noninteger, Polaris rounds
down to determine the applied value.</p>
<p>See also: pin, system, option&lt;GEOM&gt;</p>
</div>
<div class="section" id="cross-version-6-3-cross-geometry">
<span id="a-4"></span><h2>cross (Version 6.3) – cross geometry<a class="headerlink" href="#cross-version-6-3-cross-geometry" title="Permalink to this headline"></a></h2>
<div class="line-block">
<div class="line"><strong>cross</strong> hwidth=<em>Real</em> lthick=<em>Real</em>
| [Mcross=*MNAME*] [row=*Int*] [Min=*MNAME*] [ld=*Int*] [Mout=*MNAME*]</div>
</div>
<blockquote>
<div><div class="line-block">
<div class="line">[ : x<sub>1</sub> x<sub>2</sub> … x<sub>N</sub>]</div>
</div>
<div class="line-block">
<div class="line">[ : y<sub>1</sub> y<sub>2</sub> … y<sub>N</sub>]</div>
</div>
<div class="line-block">
<div class="line">[ : yin<sub>1</sub> yin<sub>2</sub> … yin<sub>N</sub>]</div>
</div>
<div class="line-block">
<div class="line">[ : nx<sub>1</sub> nx<sub>2</sub> … nx<sub>N-1</sub>]</div>
</div>
<div class="line-block">
<div class="line">[ : ny<sub>1</sub> ny<sub>2</sub> … ny<sub>N-1</sub>]</div>
</div>
</div></blockquote>
<table class="docutils align-center">
<colgroup>
<col style="width: 100%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><a class="reference internal image-reference" href="_images/3-2a-4-tab.svg"><img alt="_images/3-2a-4-tab.svg" class="align-center" src="_images/3-2a-4-tab.svg" width="600" /></a>
</td>
</tr>
</tbody>
</table>
<p>Comments:</p>
<p>The cross card performs two tasks. First, it subdivides the pinmap into
four subarrays, optionally adding a horizontal and vertical gap between
the subarrays. The row parameter is uses to subdivide the pinmap. If the
pinmap is 10×10 and row=5, each of the four subarrays is 5×5. If the
pinmap is 10×10 and row=4, the northwest subarray is 4×4, the northeast
subarray is 4×6, the southwest subarray is 6×4, and the southeast
subarray is 6×6. The hwidth parameter controls the half-spacing of the
horizontal and vertical gap in between the subarrays. The hwidth
parameter must be ≥ 0.0 and if hwidth is &gt; 0.0, the gap is filled with
material M<sub>out</sub> (default is COOL.2 with system BWR).</p>
<p>The second task is the insertion of the cross structure into the lattice
geometry. The process is described with reference to the example in Fig.
<a class="reference internal" href="#fig3-2a-4"><span class="std std-numref">Fig. 8</span></a>. In the example, the <strong>pinmap</strong> is 9×9 and row=3, hwidth=1.5,
and hspan=10.5. The top left plot contains the four following lines:</p>
<ol class="arabic simple">
<li><p>the line in the center of the vertical cross gap,</p></li>
<li><p>the line in the center of the horizontal cross gap,</p></li>
<li><p>the diagonal line from the northwest (NW) channel box corner to the
southeast (SE) corner, and</p></li>
<li><p>the diagonal line, perpendicular to line 3, passing through the
intersection of line 1 and line 2.</p></li>
</ol>
<p>These four lines intersect and form 8 separate regions, i.e., octants,
within the channel box interior. The intersection point, i.e., cross
center, is not necessarily equal to the box center as shown in this
example. In the top left plot, the red triangle represents the WNW
octant. In the bottom left plot, the red triangle represents the SSE
octant.</p>
<div class="figure align-center" id="id10">
<span id="fig3-2a-4"></span><a class="reference internal image-reference" href="_images/fig414.png"><img alt="_images/fig414.png" src="_images/fig414.png" style="width: 500px;" /></a>
<p class="caption"><span class="caption-number">Fig. 8 </span><span class="caption-text">Construction of the BWR cross geometry (full example shown later).</span><a class="headerlink" href="#id10" title="Permalink to this image"></a></p>
</div>
<p>The cross structure is defined be a series of vertices (x<sub>i</sub>,
y<sub>i</sub>). Shown as yellow points in the top left plot, the <strong>cross</strong>
vertices are defined based on an origin displayed as the red point,
which is the intersection of the inner west edge of the channel box and
the horizontal line in that passes through the cross center.</p>
<p>The top plots demonstrate how Polaris inserts a section of the cross
into the WNW octant. In the top left plot, the blue polygon is
constructed based on the first two vertices defined on the <strong>cross</strong>
card: (0.0,1.0) and (4.0,0.5). The intersection of the blue polygon and
red polygon is inserted into the lattice and filled with cross interior
material (M<sub>in</sub>). The liner is then inserted <strong>above</strong> the blue
polygon, padded by the liner thickness (lthick), and clipped by WNW red
polygon if needed.</p>
<p>Similarly, the bottom plots demonstrate insertion into the SSE octant.
For SSE insertions, the origin and the <strong>cross</strong> vertices are rotated 90
degrees about the cross center. The blue polygon is constructed from the
second and third vertices on the <strong>cross</strong> card: (4.0,0.5) and (11,0.5).
The intersection of the blue polygon and red polygon is inserted into
the lattice and filled with cross interior material (M<sub>in</sub>). The
liner is then inserted <strong>above</strong> the blue polygon, padded by the liner
thickness (lthick), and clipped by SSE red polygon if needed.</p>
<p>For each consecutive set of <strong>cross</strong> vertices, Polaris inserts a
polygonal region into each of the 8 octants. The <strong>cross</strong> vertices are
entered in the input as an x-values list followed by a y-values list of
the same length. The coordinate system of the x- and y- lists is
displayed in the top left plot of <a class="reference internal" href="#fig3-2a-4"><span class="std std-numref">Fig. 8</span></a>. The coordinate system is
transformed based on the following rules for each octant:</p>
<ul class="simple">
<li><p>WNW, ENE: no transform,</p></li>
<li><p>NNW, SSW: reflected across the diagonal line from NW to SE channel
box corners,</p></li>
<li><p>NNE, SSE: rotated 90 degrees about the cross center, and</p></li>
<li><p>ESE, WSW: reflected across the line in the center of the horizontal
cross gap.</p></li>