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  <div class="section" id="starbucs-a-scale-control-module-for-automated-criticality-safety-analyses-using-burnup-credit">
<span id="starbucs"></span><h1>STARBUCS: A Scale Control Module for Automated Criticality Safety Analyses Using Burnup Credit<a class="headerlink" href="#starbucs-a-scale-control-module-for-automated-criticality-safety-analyses-using-burnup-credit" title="Permalink to this headline"></a></h1>
<p><em>G. Radulescu and I. C. Gauld</em></p>
<p>STARBUCS is an analysis sequence in SCALE for automating criticality
safety and burnup loading curve analyses of spent fuel systems employing
burnup credit. STARBUCS requires only the fresh fuel composition, an
irradiation history, and the KENO model for a spent fuel configuration
to be provided in an input file. It automatically performs all necessary
calculations to determine spent fuel compositions, self-shielded cross
sections, and the <em>k</em><sub>eff</sub> of the spent fuel configuration. In addition,
for burnup loading curve analyses, STARBUCS performs iterative
calculations to search for initial fuel enrichments that result in an
upper subcritical limit. STARBUCS allows the user to simulate axial- and
horizontal-burnup gradients in a spent fuel assembly, select the
specific actinides and/or fission products that are to be included in
the criticality analysis, and apply isotopic correction factors to the
predicted spent fuel nuclide inventory to account for calculational bias
and uncertainties. A depletion analysis calculation for each of the
burnup-dependent regions of a spent fuel assembly, or any other system
containing spent nuclear fuel, is performed using the ORIGEN-ARP
sequence of SCALE. For criticality safety calculations employing
multigroup cross section data, the spent fuel compositions are used to
generate resonance self-shielded cross sections for each region of the
problem. The region dependent nuclide concentrations and cross sections
are applied in a three-dimensional criticality safety calculation using
the KENO code. Both KENO V.a and KENO-VI criticality codes are supported
for single criticality safety calculations using burnup credit, but only
KENO V.a can be used in criticality calculations for burnup loading
curve analyses. Although STARBUCS was developed specifically to address
the burnup-credit analysis needs for spent fuel transport and storage
applications, it provides sufficient flexibility to allow criticality
safety assessments involving many different potential configurations of
UO<sub>2</sub> spent nuclear fuel.</p>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
<p>The U.S. Nuclear Regulatory Commission (NRC) issued Revision 3 of the
Interim Staff Guidance 8 (ISG-8) (<a class="bibtex reference internal" href="#us-nuclear-regulatory-commission-burnup-2012" id="id1">[Com12]</a>) on burnup credit in
September, 2012. ISG-8 provides guidance on the application of
burnup-credit in criticality safety analyses for pressurized-water
reactor (PWR) spent fuel in transportation and storage casks. Burnup
credit is the concept of taking credit for the reduction in reactivity
in spent fuel due to burnup. The reduction in reactivity that occurs
with fuel burnup is due to the change in concentration (net reduction)
of fissile nuclides and the production of actinide and fission-product
neutron absorbers. In contrast to criticality safety analyses that
employ a fresh-fuel assumption (i.e., conservatively assuming
unirradiated fuel compositions), credit for burnup requires the
prediction of both fissile material and absorber nuclide concentrations
in spent nuclear fuel (SNF) and consideration of many burnup-related
phenomena, in addition to the criticality issues.</p>
<p>Consideration of the depletion aspects in the criticality assessment of
SNF places an increasing reliance on computational tools and methods,
and significantly increases the overall complexity of the criticality
safety analysis. The use of spent fuel nuclide concentrations in the
criticality evaluation also necessitates consideration of many
additional sources of uncertainty associated with fuel depletion. ISG-8
highlights, for example, the need for applicants employing burnup credit
in criticality safety assessments to address the axial and horizontal
variation of the burnup within a spent fuel assembly, uncertainties and
bias in the nuclide predictions, and the additional reactivity margin
available from fission products and actinides not credited in the
licensing basis.</p>
<p>To assist in performing and reviewing criticality safety assessments of
transport and storage casks that apply burnup credit, a new control
sequence called STARBUCS (<strong>St</strong>andardized <strong>A</strong>nalysis of
<strong>R</strong>eactivity for <strong>Bu</strong>rnup <strong>C</strong>redit using <strong>S</strong>CALE) was
developed in SCALE 5. STARBUCS automates the generation of
spatially-varying nuclide compositions in a spent fuel assembly, and
applies the assembly compositions in a three-dimensional (3-D)
Monte Carlo analysis of the system. STARBUCS automatically prepares
input files for each of the modules in the sequence, executes the
modules through the SCALE driver, and performs all flow control, module
interface, and data management functions. The STARBUCS sequence uses
well-established code modules currently available in SCALE. STARBUCS
also performs iterations over a range of initial fuel enrichments to
determine the initial enrichments below which UO<sub>2</sub> commercial
spent fuel may be loaded in a transport/storage cask for specified
burnup values. With this capability, STARBUCS assists in generating
burnup loading curves for criticality safety analyses of spent fuel in
transport and storage casks.</p>
<p>The STARBUCS sequence automates the depletion calculations using the
ORIGEN-ARP methodology to perform a series of cross section preparation
and depletion calculations to generate a comprehensive set of spent fuel
isotopic inventories for each spatially-varying burnup region of an
assembly. The spent fuel nuclide concentrations are subsequently input
to either CSAS5 or CSAS6 to and perform a criticality calculation of the
system using the KENO V.a or KENO-VI code, respectively, to determine
the neutron multiplication factor (<em>k</em><sub>eff</sub>) for the system. Only
minimal input is required by the user to perform a typical burnup-credit
analysis. The user can specify the assembly-average irradiation history,
the axial density variation of the reactor moderator, the axial- and
horizontal-burnup profile, and the nuclides that are to be applied in
the criticality safety analysis. Nuclide correction factors may also be
applied to the predicted concentrations to account for known bias and/or
uncertainty in the predicted SNF compositions.</p>
</div>
<div class="section" id="methodology">
<h2>Methodology<a class="headerlink" href="#methodology" title="Permalink to this headline"></a></h2>
<p>The STARBUCS control module is a burnup-credit sequence designed to
perform 3-D Monte Carlo criticality safety calculations that include the
effects of spatially-varying burnup in SNF configurations. STARBUCS
offers two options: either perform a single criticality safety
calculation with burnup credit or perform iterative calculations for
burnup loading curve analyses of commercial UO<sub>2</sub> spent fuels.
The sequence contains a set of instructions designed to automatically
process input data, execute code modules currently available in SCALE
for depletion, resonance cross section, and criticality calculations. In
addition, for burnup loading curve analyses, STARBUCS checks whether
<em>k</em><sub>eff</sub> converges to a user-provided upper subcritical limit, adjusts
the initial fuel enrichment using the least squares method, and repeats
the sequence until either convergence is achieved or determine that no
solution can be found. The overall program structures and flow for a
single criticality calculation and for burnup loading curve calculations
are illustrated in <a class="reference internal" href="#fig2-3-1"><span class="std std-numref">Fig. 17</span></a> and <a class="reference internal" href="#fig2-3-2"><span class="std std-numref">Fig. 18</span></a>, respectively.</p>
<p>The sequence uses well-established code modules currently available in
the SCALE code system. These modules include ARP and ORIGEN to perform
the depletion analysis phase of the calculations. ORIGEN-ARP is a
sequence within the SCALE system that serves as a faster alternative to
the TRITON depletion sequence of SCALE to perform point-irradiation
calculations with the ORIGEN code using problem-dependent cross
sections. ARP uses an algorithm that enables the generation of cross
section libraries for the ORIGEN code by interpolation over pregenerated
cross section libraries. The ORIGEN code performs isotopic generation
and depletion calculations to obtain the spent fuel nuclide
compositions. For criticality safety calculations using multigroup cross
section data, problem dependent cross sections are processed with the
resonance self-shielding capabilities of XSProc using the
region-dependent compositions from the depletion analyses. Finally, the
region dependent nuclide concentrations and cross sections are applied
in a 3-D criticality calculation for the system using either KENO V.a or
KENO-VI to calculate the <em>k</em><sub>eff</sub> value.</p>
<p>The ORIGEN-ARP depletion analysis methodology represents a significant
increase in computational speed as compared to equivalent calculations
performed using the SCALE depletion analysis sequences that use
two-dimensional transport methods, with virtually no sacrifice in
accuracy. ARP uses an algorithm that enables the generation of cross
sections for the ORIGEN code by interpolating on cross sections
available in pre-generated data libraries. For uranium-based fuels the
interpolation parameters available are initial fuel enrichment, burnup
and, optionally, moderator density. STARBUCS creates input files for ARP
and ORIGEN for each burnup-dependent region of an assembly and
calculates the spent fuel nuclide concentrations for the region using a
user-specified assembly irradiation history, cooling time, and burnup
profiles. The ORIGEN libraries must be available in advance of a
STARBUCS burnup-credit calculation. These libraries may be created using
TRITON. The libraries include the effects of assembly design and
operating conditions on the neutron cross sections used in the burnup
analysis. Several ORIGEN libraries are distributed in the SCALE code
system and can be applied in a STARBUCS analysis. Alternatively, a user
may create a specific ORIGEN library for other assembly types or
operating conditions not available in the default libraries. The
generation of ORIGEN reactor libraries is discussed in the ORIGEN
Reactor Libraries chapter.</p>
<p>The depletion phase of the analysis is performed using ARP and ORIGEN to
calculate the compositions of each discrete fuel region (axial or
horizontal). After a single ORIGEN-ARP depletion calculation is
completed, control is passed back to the STARBUCS module which reads the
spent fuel nuclide inventories generated by ORIGEN, saves them, prepares
the ARP and ORIGEN input files for the next burnup region, and executes
the codes in sequence. This cycle continues until the fuel compositions
for all axial and horizontal regions have been calculated and saved,
completing the depletion phase of the analysis. The depletion
calculations for each axial and radial zone are performed using an
initial fuel basis of 1 MTHM (10:sup:<cite>6</cite> g heavy metal).</p>
<p>After all depletion calculations are completed, STARBUCS reads the spent
fuel nuclide inventories for all regions and prepares input for the
criticality calculation. The concentrations of all nuclides in the
ORIGEN depletion analysis are converted from gram-atom units (per MTU)
to units of atoms/b-cm applied in the criticality calculation. The
criticality calculation is performed using the capabilities in the CSAS5
or CSAS6 control module of SCALE. Specifically, STARBUCS prepares input
for the CSAS5 module when criticality calculations are to be performed
using KENO V.a, and for the CSAS6 sequence when using KENO-VI. Note that
only the criticality safety sequence CSAS5 of SCALE can be used for
burnup loading curve calculations.</p>
<p>For burnup loading curve iterative calculations, STARBUCS employs the
search algorithm described in CSAS5 section on <em>Optimum
(Minimum/Maximum) Search</em> to determine initial fuel enrichments that
satisfy a convergence criterion for the k<sub>eff</sub> of the spent fuel
configuration. If convergence is not achieved in a search pass, the
initial fuel enrichment is automatically adjusted. This sequence repeats
until either k<em>eff</em> converges to an upper subcritical limit or until
the algorithm determines that a solution is not possible. The procedure
is repeated for each requested burnup value. The maximum allowable
iterations, upper subcritical limit, tolerance for convergence, and a
range of initial fuel enrichments can be set by the user. The lower and
upper enrichment bounds as well as the burnup values for spent fuel
regions must be contained within the range of enrichment and burnup
values used to generate the applicable ORIGEN library. The control
module prepares a STARBUCS input file for each search pass requesting a
single criticality calculation using the calculated spent fuel
compositions. In this input file, the burnup history data block and/or
the fuel mixture compositions are updated based on the outcome of the
search sequence. The pre-burnup compositions for the two minor uranium
isotopes, <sup>234</sup>U and <sup>236</sup>U, are updated in the STARBUCS
input file for a new pass only if they were included in the initial
input file prepared by the user. Their updated weight percentages are
based on the assumption that the mass ratios
<sup>234</sup>U/<sup>235</sup>U and <sup>236</sup>U/<sup>235</sup>U do not
change with fuel enrichment.</p>
<div class="figure align-center" id="id7">
<span id="fig2-3-1"></span><a class="reference internal image-reference" href="_images/fig1104.png"><img alt="_images/fig1104.png" src="_images/fig1104.png" style="width: 600px;" /></a>
<p class="caption"><span class="caption-number">Fig. 17 </span><span class="caption-text">Modules and flow of STARBUCS sequence for criticality calculations.</span><a class="headerlink" href="#id7" title="Permalink to this image"></a></p>
</div>
<div class="figure align-center" id="id8">
<span id="fig2-3-2"></span><a class="reference internal image-reference" href="_images/fig216.png"><img alt="_images/fig216.png" src="_images/fig216.png" style="width: 600px;" /></a>
<p class="caption"><span class="caption-number">Fig. 18 </span><span class="caption-text">Modules and flow of STARBUCS sequence for burnup loading curve calculations.</span><a class="headerlink" href="#id8" title="Permalink to this image"></a></p>
</div>
</div>
<div class="section" id="capabilities-and-limitations">
<span id="cap-and-lim"></span><h2>Capabilities and Limitations<a class="headerlink" href="#capabilities-and-limitations" title="Permalink to this headline"></a></h2>
<p>STARBUCS is designed to facilitate criticality safety analyses employing
burnup credit by automating and linking the depletion and criticality
calculations. The STARBUCS sequence has been designed to readily allow
analysts and reviewers to assess the subcritical margins associated with
many of the important phenomena that need to be evaluated in the context
of the current regulatory guidance on burnup credit. However, STARBUCS
is sufficiently general to allow virtually any configuration involving
irradiated nuclear material to be analyzed. Limitations and some of the
key capabilities of the STARBUCS sequence are described below.</p>
<ol class="arabic simple">
<li><p>STARBUCS limitations include the use of a single UO<sub>2</sub> fuel
type and, for analyses employing multigroup cross section data, the
use of geometry configurations consisting of spent fuel rod arrays.
However, the type of spent fuel configurations that can be analyzed
is entirely general. STARBUCS can be used to perform criticality
safety assessments of individual fuel assemblies, a spent fuel cask,
a spent fuel storage pool, or any nuclear system containing
UO<sub>2</sub> irradiated nuclear fuel.</p></li>
<li><p>Only the criticality safety sequence CSAS5 of SCALE can be used for
burnup loading curve calculations; therefore KENO V.a geometry
description must be available in a STARBUCS input file for burnup
loading curve calculations.</p></li>
<li><p>Burnup calculations can incorporate any desired operating history.
The user may enter the specific power, cycle lengths, cycle down
time, post-irradiation cooling time, etc. The axial-water-moderator
density variation may also be specified in the depletion analysis,
provided the ORIGEN cross section library contains such data.</p></li>
<li><p>The effects of assembly design, soluble boron concentrations,
burnable poison exposure, reactor operating conditions, etc., are
accounted for in the ORIGEN cross section libraries used in the
ORIGEN depletion calculations. Libraries for several fuel assembly
designs are distributed with SCALE. These libraries can also be
readily created for any reactor and fuel assembly design that can be
represented in the depletion analysis sequences of the SCALE system.</p></li>
<li><p>The user can select the specific actinide and/or fission product
nuclides to be included in the criticality safety analysis. The user
also has the option to perform a criticality calculation employing
all nuclides for which cross section data exist.</p></li>
<li><p>Isotopic correction factors may be input to adjust the calculated
nuclide inventories to account for known bias and/or uncertainties
associated with the depletion calculations.</p></li>
</ol>
<p>Minimal user input is required to perform many types of analyses.
Default values are supplied for many of the input parameter keywords.
The user may select from built-in burnup-dependent 18-axial-zone
profiles taken from <a class="bibtex reference internal" href="#lancaster-actinide-only-1998" id="id2">[LFKR98]</a>, or the user may input an arbitrary
user-defined burnup distribution with up to 100-axial zones and up to
7-horizontal zones. The depletion analysis calculations for each zone
are performed for all nuclides (the ORIGEN data libraries contain cross
section and decay data for more than 1000 unique actinides, fission
products, and structural activation products). The specific nuclides to
be considered in the <em>k</em><sub>eff</sub> analysis may be input by the user. If no
nuclide set is explicitly selected, then all nuclides that have cross
section data in the ORIGEN library are automatically applied in the
criticality analysis, resulting in a “full” burnup-credit criticality
assessment. A capability to adjust the calculated isotopic inventories
using correction factors that can account for biases and/or
uncertainties in the calculated isotopic concentrations is also
provided.</p>
<p>An appropriate ORIGEN cross section library for UO<sub>2</sub> fuel must
be available for the depletion analysis using STARBUCS. The user may use
the libraries distributed with SCALE (e.g., ge7×7-0, ge8×8-4, ce14×14,
w15×15, w17×17_ofa) or the user may generate their own problem-specific
libraries using the TRITON depletion analysis sequence available in
SCALE. A complete list of ORIGEN libraries distributed with SCALE and
methods for generating ORIGEN libraries are both described in the ORIGEN
Reactor Libraries chapter. The range of initial fuel enrichment and
requested burnup values to be used in the STARBUCS calculations must be
contained within the range of the enrichments and burnups used to
generate the applicable ORIGEN library.</p>
<p>The user is required to provide a complete KENO V.a model of the spent
fuel configuration for burnup loading curve calculations and a complete
KENO V.a or KENO-VI model of the spent fuel configuration for single
criticality calculations using burnup credit. The initial material
composition information is defined in a standard composition data block.
The fuel material is automatically depleted in the sequence for each of
the burnup-dependent regions or zones in the problem. The nuclide
concentrations after irradiation and decay are automatically applied to
the KENO criticality analysis. The mixture numbers for each of the fuel
regions are identified by unique mixture numbers assigned automatically
by STARBUCS based on the axial and horizontal regions in the problem
(see <a class="reference internal" href="#fig2-3-3"><span class="std std-numref">Fig. 19</span></a>). The user is required to specify the geometry/extent
of the axial and horizontal zones in the KENO model and apply the
appropriate mixture numbers for the desired configuration based on the
mixture identifying scheme. STARBUCS performs no checking of the
criticality model to verify that all mixtures in the problem have been
used or that the order of the mixture numbers in the KENO model
corresponds to the corresponding order of the input burnup profile. This
provides the user a great deal of flexibility in setting up problems.
However, it also requires that the user accurately prepare the input
files to ensure that the spent fuel zone mixtures are assigned to the
correct KENO V.a or KENO-VI geometry regions. For instance, the user
could (intentionally) reverse the order of the axial-material
identifiers in the KENO model to simulate inverted fuel, or zone
mixtures could be omitted to simulate a problem using only a subset of
the available fuel zones that were simulated in the depletion analysis.</p>
<div class="figure align-center" id="id9">
<span id="fig2-3-3"></span><a class="reference internal image-reference" href="_images/fig315.png"><img alt="_images/fig315.png" src="_images/fig315.png" style="width: 600px;" /></a>
<p class="caption"><span class="caption-number">Fig. 19 </span><span class="caption-text">Fuel and material mixture numbering convention used in STARBUCS.</span><a class="headerlink" href="#id9" title="Permalink to this image"></a></p>
</div>
<div class="figure align-center" id="id10">
<span id="fig2-3-4"></span><a class="reference internal image-reference" href="_images/fig415.png"><img alt="_images/fig415.png" src="_images/fig415.png" style="width: 600px;" /></a>
<p class="caption"><span class="caption-number">Fig. 20 </span><span class="caption-text">Example of mixture numbering scheme used in STARBUCS.</span><a class="headerlink" href="#id10" title="Permalink to this image"></a></p>
</div>
<p>There are several conventions that must be followed when using STARBUCS.
In general, these relate to the specification of materials and mixture
numbering of the cross section mixing table.</p>
<ol class="arabic simple">
<li><p>The maximum number of horizontal zones is restricted to seven if
there is no gap or second moderator mixture, six if a gap or second
moderator mixture is defined, and five if both a gap and a second
moderator are defined. The number of axial-fuel zones is limited such
that the product of horizontal zones ∗ axial zones is less than or
equal to 100. These limits constrain the maximum mixture number used
for burned fuel in the KENO criticality calculation to less than 1000
and assign unique mixture numbers to clad, moderator, and gap
mixtures for lattice cell descriptions. The convention used to number
the depleted fuel zones is to start at mixture 101 and increment by 1
for each axial-burnup region. Thus, for a case with 10 axial-burnup
regions, the fuel mixtures used in the criticality analysis would
range from 101 to 110. For a similar case having two horizontal zones
in addition to the axial zones, the mixture numbers would also
include mixtures 201 to 210.</p></li>
<li><p>Mixture numbers for the clad, gap (if applicable), and moderator may
also be used directly in the KENO model. Additional unique mixture
numbers are required by the code for the lattice cell descriptions
for each separate fuel zone (except for mixture 0 for void). These
additional mixtures are assigned automatically by the code and are
shown in <a class="reference internal" href="#fig2-3-3"><span class="std std-numref">Fig. 19</span></a> for a lattice cell consisting of fuel, gap,
clad, and moderator. The additional mixture numbers may also be used
directly in the KENO model. Mixture number allocation is illustrated
in <a class="reference internal" href="#fig2-3-4"><span class="std std-numref">Fig. 20</span></a> for an example case where the number of different
horizontal zones is four and the maximum number of axial zones is
limited to 25.</p></li>
<li><p>All structural materials in the problem must have mixture numbers
different from the numbers automatically generated by the code (see
<a class="reference internal" href="#fig2-3-4"><span class="std std-numref">Fig. 20</span></a> for an example of available mixture numbers). For the
example shown in <a class="reference internal" href="#fig2-3-4"><span class="std std-numref">Fig. 20</span></a>, mixtures 5–100, 126–200, 226–300,
326–400, 501, 601, 701, 426–500, and 801–2147 are not allocated by
STARBUCS and may be defined by the user in the composition data block
and used in the geometry model. If the constraints in paragraph 1 are
followed, mixture numbers less than 100 that were not used for fuel,
gap, clad, moderator and mixture numbers from 1001 to 2147 are always
available for structural materials. Note that STARBUCS does not
provide a warning or stop program execution if a mixture number
assigned to a structural material has also been generated internally
by the computer code. The mixture numbers for structural materials
are not changed and are thus applied in the KENO model in a
one-to-one correspondence with the standard composition mixture as
done for typical CSAS calculations. Therefore, the use of a mixture
number for structural materials that is identical to one of the
mixture numbers automatically generated by the code results in the
combination of both materials in the composition for the mixture
number.</p></li>
<li><p>Not all SCALE standard composition alphanumeric names (see the
Standard Composition Library chapter) are currently recognized by
STARBUCS. The use of special materials (e.g., C-GRAPHITE, NIINCONEL,
H-POLY), particularly as fuel materials, that have nuclide
identifiers that are not readily translated to ORIGEN ZA numbers
should be avoided since these materials cannot be depleted.</p></li>
<li><p>A single STARBUCS calculation is limited to a single initial fuel
type (composition, enrichment, assembly design, etc.). Configurations
involving multiple fuel types may be solved by running a separate
STARBUCS case for each type, saving the corresponding CSAS cases
generated by STARBUCS that contain the irradiated fuel nuclide
compositions, and manually merging the cases in such a way that all
required fuel types are represented in the final case.</p></li>
</ol>
</div>
<div class="section" id="input-description">
<h2>Input Description<a class="headerlink" href="#input-description" title="Permalink to this headline"></a></h2>
<p>STARBUCS input is divided into different data blocks containing related
types of information. The standard composition data block used to define
initial (fresh) fuel composition and all other materials in the
criticality analysis problem, is read and processed by the material and
cross section processing module of SCALE (XSProc) and conforms to the
standard input conventions (see
Chapter 7 (SECTIONREFERENCE)
In addition to the standard composition data, three more input data
blocks are required by STARBUCS. The data blocks are entered in the form</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="err">READ</span> <span class="err">XXXX</span>    <span class="err">input</span> <span class="err">data</span>   <span class="err">END</span> <span class="err">XXXX</span>
</pre></div>
</div>
<p>where <strong>XXXX</strong> is the data block keyword for the type of data being
entered. The types of data blocks that are entered include general
control parameter information, irradiation history and decay data or
search parameter data, and the KENO V.a or KENO-VI input specifications.
The valid block keywords for a single criticality safety calculation
using burnup credit and for burnup loading curve calculations are listed
in <a class="reference internal" href="#tab2-3-1"><span class="std std-numref">Table 9</span></a> and <a class="reference internal" href="#tab2-3-2"><span class="std std-numref">Table 10</span></a>, respectively. A minimum of four
characters is required for most keywords. The exception is the
criticality model input data block READ KENOVA or READ KENOVI in which
case the code must check additional character positions to determine the
CSAS control sequence to be executed. The keywords can be up to twelve
characters long, the first four of which must be input exactly as listed
in the table. Entering the words <strong>READ XXXX</strong> followed by one or more
blanks activates the data block input. All input data pertinent to block
<strong>XXXX</strong> are then entered. Entering <strong>END XXXX</strong> followed by two or more
blanks terminates data block <strong>XXXX</strong>.</p>
<span id="tab2-3-1"></span><table class="docutils align-center" id="id11">
<caption><span class="caption-number">Table 9 </span><span class="caption-text">Valid data block keywords for a single criticality safety calculation using burnup credit</span><a class="headerlink" href="#id11" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><strong>Data block type</strong></p></td>
<td><p><strong>Block keyword</strong></p></td>
</tr>
<tr class="row-even"><td><p>Control parameters</p></td>
<td><p>CONTROL</p></td>
</tr>
<tr class="row-odd"><td><p>Burnup history</p></td>
<td><p>HISTORY or BURNDATA</p></td>
</tr>
<tr class="row-even"><td><p>KENO V.a input</p></td>
<td><p>KENOVA or KENO5</p></td>
</tr>
<tr class="row-odd"><td><p>KENO-VI input</p></td>
<td><p>KENOVI or KENO6</p></td>
</tr>
</tbody>
</table>
<span id="tab2-3-2"></span><table class="docutils align-center" id="id12">
<caption><span class="caption-number">Table 10 </span><span class="caption-text">Valid data block keywords for burnup loading curve calculations.</span><a class="headerlink" href="#id12" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 53%" />
<col style="width: 48%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><strong>Data block type</strong></p></td>
<td><p><strong>Block keyword</strong></p></td>
</tr>
<tr class="row-even"><td><p>Control parameters</p></td>
<td><p>CONTROL</p></td>
</tr>
<tr class="row-odd"><td><p>Search parameters</p></td>
<td><p>SEARCH</p></td>
</tr>
<tr class="row-even"><td><p>KENO V.a input</p></td>
<td><p>KENOVA or KENO5</p></td>
</tr>
</tbody>
</table>
<p>All input within a data block is entered using keywords and is free
format. Keyword entries may be of variable or array type. Variable
keyword entries include the keyword plus the “=”, followed by the value.
Array keywords are usually followed by a series of entries, each
separated by a blank or comma, and must always be terminated with an END
that does not begin in column one. In some instances a single value may
be input as an array entry; however, the word END is still always
required. Within a given input data block the keyword entries may be in
any order.</p>
<p>A single data entry may be entered anywhere on a line but cannot be
divided between two lines; however, array data entries may be divided
over many lines. The code identifies data keywords using only the first
four (maximum) characters in the keyword name. Beyond the first four
characters, the user may enter any alphanumeric or special character
acceptable in FORTRAN, including single blanks, before the “=”
character. Floating-point data may be entered in various forms; for
example, the value 12340.0 may be entered as: 12340, 12340.0, 1.234+4,
1.234E+4, 1.234E4, or 1.234E+04. Also, the value 0.012 may be entered as
12E−3, 12−3, 1.2−2, etc. Numeric data must be followed immediately by
one or more blanks or a comma.</p>
<div class="section" id="overview-of-input-structure">
<h3>Overview of input structure<a class="headerlink" href="#overview-of-input-structure" title="Permalink to this headline"></a></h3>
<p>An overview of the input to the STARBUCS sequence is given in
<a class="reference internal" href="#tab2-3-3"><span class="std std-numref">Table 11</span></a>. This table provides an outline of the input data block
structure. The input data in positions 1 to 5 (see <a class="reference internal" href="#tab2-3-3"><span class="std std-numref">Table 11</span></a>) are read
and processed by the material and cross section processing module of
SCALE (XSProc). These are the first data read by the code and must be in
the order indicated. Data positions 6, 7 or 8, and 9 are read directly
by STARBUCS and may be entered in any order.</p>
<span id="tab2-3-3"></span><table class="docutils align-center" id="id13">
<caption><span class="caption-number">Table 11 </span><span class="caption-text">Outline of input data for the STARBUCS sequence</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>
<tbody>
<tr class="row-odd"><td><p><strong>Data</strong></p>
<p><strong>position</strong></p>
</td>
<td><p><strong>Type of
data</strong></p></td>
<td><p><strong>Data entry</strong></p></td>
<td><p><strong>Comments</strong></p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Sequence name</p></td>
<td><p>=STARBUCS</p></td>
<td><p>Start in column
one</p></td>
</tr>
<tr class="row-odd"><td><p>1</p></td>
<td><p>TITLE</p></td>
<td><p>Enter a title</p></td>
<td><p>80 characters</p></td>
</tr>
<tr class="row-even"><td><p>2</p></td>
<td><p>Standard SCALE
pointwise or
multigroup
cross section
library name or</p>
<p>the name of a
user-supplied
multigroup
cross section
library</p>
</td>
<td><p>Library name</p></td>
<td><p>The currently
available
standard SCALE
cross section
libraries are
listed in the
SCALE Cross
Section
Libraries
chapter, table
<em>Standard SCALE
Cross-Section
Libraries</em>.</p>
<p>STARBUCS allows
a non-standard
SCALE
multigroup
cross section
library to be
used in a
criticality
calculation.</p>
</td>
</tr>
<tr class="row-odd"><td><p>3</p></td>
<td><p>Standard
Composition
specification
data</p></td>
<td><p>Enter the
appropriate
data</p></td>
<td><p>Begins this
data block with
READ COMP and
terminate with
END COMP. See
Standard
Composition
section for
details.</p></td>
</tr>
<tr class="row-even"><td><p>4</p></td>
<td><p>Type of
calculation</p></td>
<td><p>LATTICECELL</p></td>
<td><p>Begins this
data block with
READ CELL and
terminates with
END CELL. Only
regular unit
cells may be
used. See
XSProc section
for details.</p></td>
</tr>
<tr class="row-odd"><td><p>5</p></td>
<td><p>Unit cell
geometry
specification<sup>a</sup></p></td>
<td><p>Enter the
appropriate
data</p></td>
<td><p>Each dimension
may be entered
as a diameter.
See XSProc
section for
LATTICECELL.</p></td>
</tr>
<tr class="row-even"><td><p>6</p></td>
<td><p>Control
parameter data</p></td>
<td><p>Enter the
desired data</p></td>
<td><p>Begins this
data block with
READ CONT and
terminate with
END CONT.
See Conntrol parameter data sec</p></td>
</tr>
<tr class="row-odd"><td><p>7<sup>b</sup></p></td>
<td><p>Burnup history
specification</p></td>
<td><p>Enter the
desired data
for each cycle</p></td>
<td><p>Begins this
data block with
READ HISTORY
(or BURNDATA)
and terminate
with
END HISTORY (or
BURNDATA).
See Burnup hist/
ory data sec.</p></td>
</tr>
<tr class="row-even"><td><p>8<sup>b</sup></p></td>
<td><p>Search
parameter data</p></td>
<td><p>Enter the
desired data</p></td>
<td><p>Begins this
data block with
READ SEARCH and
terminate with
END SEARCH.
See Search para/
meter data sec.</p></td>
</tr>
<tr class="row-odd"><td><p>9</p></td>
<td><p>KENO data</p></td>
<td><p>Enter KENO
criticality
model</p></td>
<td><p>Begins this
data block with
READ KENOVA (or
KENO5) and
terminate with
END KENOVA (or
KENO5).</p>
<p>For KENO-VI use
block keyword
KENOVI (or
KENO6) in place
of KENOVA
(or KENO5). See
Keno Input Data.</p>
</td>
</tr>
<tr class="row-even"><td></td>
<td><p>Terminate input</p></td>
<td><p>END</p></td>
<td><p>Must begin in
column 1.</p></td>
</tr>
<tr class="row-odd"><td><p><sup>a</sup> Input
data required only for criticality calculations employing
multigroup
cross section
libraries. Only
one unit cell
may be defined
in the cell
data block for
STARBUCS.</p>
<p><sup>b</sup> Either
burnup history
specification
or search
parameter data
may be defined
in a STARBUCS
input.</p>
</td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="sequence-specification-card">
<h3>Sequence specification card<a class="headerlink" href="#sequence-specification-card" title="Permalink to this headline"></a></h3>
<p>The STARBUCS analytical sequence is initiated with “=STARBUCS” beginning
in column 1 of the input. This instructs the SCALE driver module to
execute the STARBUCS sequence. The input data are then entered in
free-format. The input is terminated with the word “END” starting in
column 1. An “END” is a special data item, which may be used to delimit
an input data block, end an array of input items, and terminate the
input for the case. In the context of input data blocks, the “END” has a
name or label associated with it. An “END” used to terminate an array of
entries must not begin in column 1 as this instructs the SCALE driver to
terminate input to the sequence.</p>
</div>
<div class="section" id="optional-sequence-parameters">
<h3>Optional sequence parameters<a class="headerlink" href="#optional-sequence-parameters" title="Permalink to this headline"></a></h3>
<p>To check the input data, run STARBUCS and specify PARM=CHECK or PARM=CHK
after the analytical sequence specification as shown below.</p>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=STARBUCS PARM=CHK</span>
</pre></div>
</div>
<p>Other optional input for the PARM field to control multigroup resonance
self-shielding calculations are described in the XSProc section of this
manual.</p>
</div>
<div class="section" id="xsproc">
<h3>XSProc<a class="headerlink" href="#xsproc" title="Permalink to this headline"></a></h3>
<p>The XSProc is used to read and process the standard composition
specification data that define the initial compositions of the fuel and
all structural materials in the problem, into mixing tables and unit
cell geometry information that are used by STARBUCS. All composition
data required for the problem are entered as standard composition
entries. A detailed description of this portion of the input can be
found in the section on XSProc (Chapter 7 (SECTIONREFERENCE)). Only one UO<sub>2</sub> fuel
type is permitted in STARBUCS. Therefore, a single fuel mixture defining
the fresh fuel composition and, for criticality safety calculations
employing multigroup cross sections, the geometry description of a
single fuel lattice cell are required in a STARBUCS input file. Only the
regular unit cells SQUAREPITCH, TRIANGPITCH, SPHSQUAREP, SPHTRIANGP, and
SYMMSLACELL may be specified for the LATTICECELL entry. Outside
diameters of the fuel, gap, and clad mixtures (i.e., not the radii) are
required.</p>
</div>
<div class="section" id="control-parameter-data">
<h3>Control parameter data<a class="headerlink" href="#control-parameter-data" title="Permalink to this headline"></a></h3>
<p>The control parameter data block allows the user to specify control
parameters and array data related to many of the burnup-credit analysis
parameters to be used in the problem. All input is by keyword entry. All
keywords are three-character identifiers that must be followed
immediately by an equals sign (“=”). The keywords may be in any order
within a data block. Input to the parameter data block is initiated with
the data block keywords <strong>READ CONTROL</strong> (only first four characters of
block name are required). The data block is terminated by the keywords
<strong>END CONTROL</strong>.</p>
<p>The types of control parameter data that may be input are summarized in
Table 2.3.4. The individual keyword entries are described below.</p>
<ol class="arabic simple">
<li><p>ARP= NAME OF THE ORIGEN LIBRARY TO BE USED. A character string with
the name of the ORIGEN library to be used in the depletion
calculation. This is a required entry. The library must be defined
in the SCALE text file ARPDATA.TXT that contains the cross section
library names and interpolation data used by ARP. A description of
an ARP input and the location of the ORIGEN cross section libraries
are provided in <em>ARP Input Description</em> located in the ORIGEN ARP
Module chapter. STARBUCS calculations are limited to UO<sub>2</sub>
spent fuels.</p></li>
<li><p>NAX= NUMBER OF AXIAL ZONES. This is the number of axial-burnup
subdivisions. For a user-input profile the value of NAX is
determined automatically by the code, and the NAX keyword is
optional, provided the AXP= array has been entered. The maximum
value of NAX must be chosen such that due product of NAX * NHZ is
less than or equal to 100 (i.e., NAX:sub:<cite>max</cite> is 100, 50, 33, 25,
20, 16, or 14 when the number of horizontal zones is 1, 2, 3, 4, 5,
6, or 7, respectively). By default, the profile is automatically
normalized to unity by the code unless NPR=no. Built-in
burnup-dependent 18‑axial-zone profiles may be selected with an
entry of –18. These built-in profiles and the burnup range over
which they are applied, are listed in <a class="reference internal" href="#tab2-3-5"><span class="std std-numref">Table 13</span></a>. These profiles
have been proposed elsewhere (Ref. 2) as bounding axial profiles and
are included as options for convenience only. The default value of
NAX is –18 (use built-in profiles).</p></li>
<li><p>NHZ= NUMBER OF HORIZONTAL ZONES. This is the number of
horizontal-burnup subdivisions in the assembly. An optional entry if
no horizontal profile is requested. The maximum value is seven
zones. The exact limit is determined by the number of mixtures
defined in the lattice cell description. If a gap and second
moderator type are used the number of horizontal zones is limited to
five.</p></li>
<li><p>NUC= BURNUP-CREDIT NUCLIDES used in the criticality calculation. A
list of actinides and/or fission products that are to be included in
the KENO criticality safety calculation. This is an array entry
keyword and is delimited by the keyword END. The nuclides are
entered using their standard composition alphanumeric names, as
listed in the Standard Composition Library chapter of the SCALE
manual. Isotopic correction factors may be entered, optionally,
immediately following the nuclide name. The isotopic correction
factors will be multiplied times the spent fuel nuclide
concentrations to account for isotopic composition bias.
The concentration of any nuclide that does not have a correction
factor is not adjusted. To select all available actinide and fission
product nuclides (with cross section data and atom densities greater
than 1.0E−29) for the criticality calculation, the user may select
NUC= ALL, without an END terminator. This is the only situation
where an array entry does not require an END. Note that the set of
nuclides tracked by ORIGEN in any decay or irradiation calculation,
documented in the ORIGEN Reaction Resource Contents chapter, is much
larger than the set of nuclides with available cross sections for
neutron transport calculations, documented in the SCALE Cross
Section Libraries chapter. Only nuclides with available cross
sections for neutron transport calculations are included in the
irradiated fuel compositions for criticality calculations.</p></li>
<li><p>FLE= FUEL LIGHT ELEMENT NUCLIDES. A user-provided list of light
element nuclides that are to be included in the irradiated fuel
compositions for a CSAS5 or a CSAS6 calculation. This is an array
entry keyword and is delimited by the keyword END. The nuclides are
entered using their standard composition alphanumeric names, as
listed in Standard Composition Library chapter of the SCALE manual.
To select all available light element nuclides (with cross section
data and atom densities greater than 1.0E−29) for the criticality
calculation, the user may specify FLE= ALL, without an END
terminator. This is the only situation where an array entry does not
require an END. The use of the keyword FLE is not required if only
o-16 is to be included in the composition of irradiated uranium
oxide fuel pellets. For these material mixtures, o-16 will be
automatically included in irradiated fuel compositions due to its
significant concentration. Isotopic correction factors are not
allowed for light element nuclides. Note that the set of nuclides
tracked by ORIGEN in any decay or irradiation calculation,
documented in the ORIGEN Reaction Resource Contents chapter, is much
larger than the set of nuclides with available cross sections for
neutron transport calculations, documented in the SCALE Cross
Section Libraries chapter. Only nuclides with available cross
sections for neutron transport calculations are included in the
irradiated fuel compositions for criticality calculations.</p></li>
<li><p>AXP= AXIAL-BURNUP PROFILE. The user-supplied axial-burnup profile of
the assembly to be used in the analysis. This entry is required
unless use of the built-in burnup-dependent axial profiles shown in
<a class="reference internal" href="#tab2-3-5"><span class="std std-numref">Table 13</span></a> is requested (NAX= −18). If NAX is set to anything other
than −18, the AXP array must contain NAX entries. Otherwise, the
value of NAX is determined automatically by the code. By default
(NPR=yes), the profile is automatically normalized by the code; this
may be disabled by setting NPR=no. If the burnup profile is
normalized, it is implicitly assumed that the height/volume of each
axial region is uniform when determining the average fuel burnup
(i.e., the burnup of each axial region is equally weighted). <strong>The
user is cautioned that if fuel region subdivisions of unequal volume
are used, normalization should not be applied and the user must
ensure a correct correspondence between the axial-profile input and
the axial regions specified in the criticality calculation. AXP</strong> is
an array entry and must be delimited by an END that must not start
in the first column.</p></li>
<li><p>HZP= HORIZONTAL-BURNUP PROFILE. An optional array entry used to
specify a burnup gradient across assemblies. The elements of the
array are the ratios of the burnups of horizontal subdivisions in
the assembly to average assembly burnup (entry for the POWER=
keyword described in <a class="reference internal" href="#burnup-history-data"><span class="std std-ref">Burnup history data</span></a>). If NHZ is input, the HZP array
must contain NHZ entries delimited by an END that must not start in
the first column. Otherwise, the value of NHZ is determined
automatically by the code. The profile will be normalized if NPR=yes
(default). Sample problem 5 illustrates use of this option.</p></li>
<li><p>FIX= FIXED ASSEMBLY POWER OPTION. Option to select a constant
specific power level for the depletion analysis for all axial and
horizontal zones of the assembly. For FIX=yes, the depletion
analysis for all zones is performed using the specific power input
in the power history data block for the POWER= keyword. The
irradiation time is adjusted to achieve the desired burnup. The
default of FIX=no applies a variable power for all zones and a
constant irradiation time as defined by the BURN= keyword.</p></li>
<li><p>NPR= NORMALIZE PROFILE. Option to control whether the user input
axial- and horizontal-burnup profiles will be normalized. The input
profiles are automatically normalized using NPR=yes (default). If
fuel region subdivisions of unequal volume are used, NPR=NO should
be specified.</p></li>
<li><p>MOD= AXIAL MODERATOR DENSITY. This is an array entry keyword and is
delimited by the keyword END. The array dimension is equal to the
number of axial zones (NAX entry) and the array values are provided
in the same order as the AXP array elements. This input array is
required only if the applicable ORIGEN library contains variable
moderator density cross sections.</p></li>
<li><p>BUG= DEBUG PRINT OPTION. BUG=yes will print program debugging
variables and arrays in STARBUCS. The default is BUG=no.</p></li>
</ol>
<span id="tab2-3-4"></span><table class="docutils align-center" id="id14">
<caption><span class="caption-number">Table 12 </span><span class="caption-text">Table of control parameter data.</span><a class="headerlink" href="#id14" 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>
<tbody>
<tr class="row-odd"><td><p><strong>Keyword</strong></p>
<p><strong>name</strong></p>
</td>
<td><p><strong>Data</strong></p>
<p><strong>type</strong></p>
</td>
<td><p><strong>Default</strong></p>
<p><strong>value</strong></p>
</td>
<td><p><strong>Comments</strong></p></td>
</tr>
<tr class="row-even"><td><p>READ CONTROL</p></td>
<td></td>
<td><p>Initiate
reading the
control
parameter block
of data</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>ARP=</p></td>
<td><p>Character</p></td>
<td><p>None</p></td>
<td><p>Name of the
ORIGEN library
to be used.
Required.
Library must be
defined in
SCALE text file
ARPDATA.TXT.</p></td>
</tr>
<tr class="row-even"><td><p>NAX=</p></td>
<td><p>Integer</p></td>
<td><p>−18</p></td>
<td><p>Number of
axial-burnup
subdivisions in
fuel assembly.
The value of
NAX is
determined
automatically
if an axial
profile is
input using
AXP= entries.
The maximum
value of NAX is
100. Default
value (−18)
applies a
built-in
18‑axial-region
-burnup
profile.</p></td>
</tr>
<tr class="row-odd"><td><p>NHZ=</p></td>
<td><p>Integer</p></td>
<td><p>1</p></td>
<td><p>Number of
horizontal-burn
up
subdivisions.
Maximum value
of
5–7 zones (see
Sect. 2.3.4.5).
No entry is
required if
horizontal
profile is not
used.</p></td>
</tr>
<tr class="row-even"><td><p>NUC=</p></td>
<td><p>Character and
real mixed
array<sup>a</sup></p></td>
<td><p>None</p></td>
<td><p>List of
burnup-credit
nuclides, and
optionally the
corresponding
isotopic
correction
factors, to be
included in the
criticality
calculation.<sup>b</sup>
Array entry
generally
delimited by
END, unless ALL
is selected.
Nuclides are
input using
their standard
composition
alphanumeric
identifiers.</p></td>
</tr>
<tr class="row-odd"><td><p>FLE=</p></td>
<td><p>Character
array<sup>a</sup></p></td>
<td><p>o-16</p></td>
<td><p>List of light
element
nuclides to be
included in the
criticality
calculation.<sup>b</sup>
Array entry
generally
delimited by
END, unless ALL
is selected.
Nuclides are
input using
their standard
composition
alphanumeric
identifiers.</p></td>
</tr>
<tr class="row-even"><td><p>AXP=</p></td>
<td><p>Real array<sup>a</sup></p></td>
<td><p>See NAX</p></td>
<td><p>Axial-burnup-pr
ofile
array. Required
if NAX &gt; 0. NAX
entries that
define the
axial-burnup
shape. The
profile is
automatically
normalized if
NPR=YES
(default).
Delimited by
END.</p></td>
</tr>
<tr class="row-odd"><td><p>HZP=</p></td>
<td><p>Real array<sup>a</sup></p></td>
<td><p>None</p></td>
<td><p>Horizontal-burn
up-profile
array. Required
if NHZ &gt; 1.
Array containin
g
NHZ entries
that define the
horizontal,
or radial,
burnup profile
for the
analysis. Array
is
automatically
normalized by
the code.
Delimited by
END.</p></td>
</tr>
<tr class="row-even"><td><p>MOD=</p></td>
<td><p>Real array<sup>a</sup></p></td>
<td><p>None</p></td>
<td><p>Axial-moderator
density,
applied in the
fuel depletion
analysis.
Note that MOD=
is required
only if the
ORIGEN library
contains
variable
moderator
density cross
sections.
NAX entries
ordered as AXP=
array.
Delimited by
END. Moderator
density default
values are not
available in
STARBUCS for
variable
moderator
density cross
sections.</p></td>
</tr>
<tr class="row-odd"><td><p>FIX=</p></td>
<td><p>Character</p></td>
<td><p>No</p></td>
<td><p>Option to
select a
constant
specific power
level for all
axial and
horizontal
zones of the
assembly using
FIX=yes.</p></td>
</tr>
<tr class="row-even"><td><p>NPR=</p></td>
<td><p>Character</p></td>
<td><p>Yes</p></td>
<td><p>Option to
normalize
user-input
axial- and
horizontal-burn
up
profiles.
Default is to
automatically
normalize
profiles.</p></td>
</tr>
<tr class="row-odd"><td><p>BUG=</p></td>
<td><p>Character</p></td>
<td><p>No</p></td>
<td><p>Optional debug
printout with
BUG=yes.</p></td>
</tr>
<tr class="row-even"><td><p>END CONTROL</p></td>
<td></td>
<td><p>End of the
control
parameter block
of data</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><dl class="simple">
<dt><sup>a</sup> Termina</dt><dd><p>te array data
entries with
end. Do not
place this end
in column 1.</p>
</dd>
<dt><sup>b</sup> Note th</dt><dd><p>at the set of
nuclides
tracked by
ORIGEN in any
decay or
irradiation
calculation,
documented in
the ORIGEN
Reaction
Resource
Contents
chapter, is
much larger
than the set of
nuclides with
available cross
sections for
neutron
transport
calculations,
documented in
the SCALE Cross
Section
Libraries
chapter. Only
nuclides with
available cross
sections for
neutron
transport
calculations
are included in
the irradiated
fuel
compositions
for criticality
calculations.</p>
</dd>
</dl>
</td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
<span id="tab2-3-5"></span><table class="docutils align-center" id="id15">
<caption><span class="caption-number">Table 13 </span><span class="caption-text">Built-in burnup-dependent axial profiles, NAX= 18 from <a class="bibtex reference internal" href="#lancaster-actinide-only-1998" id="id3">[LFKR98]</a>)</span><a class="headerlink" href="#id15" title="Permalink to this table"></a></caption>
<colgroup>
<col style="width: 20%" />
<col style="width: 20%" />
<col style="width: 20%" />
<col style="width: 20%" />
<col style="width: 20%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><strong>Axial</strong></p>
<p><strong>zone
no.</strong></p>
</td>
<td><p><strong>Fraction
of</strong></p>
<p><strong>core
height</strong></p>
</td>
<td><p><strong>Burnup
&lt; 18 GWd/MT
U</strong></p></td>
<td><p><strong>18 ≤
Burnup
&lt; 30 GWd/MT
U</strong></p></td>
<td><p><strong>Burnup
≥ 30 GWd/MT
U</strong></p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td><p><strong>1</strong></p></td>
<td><p><strong>2</strong></p></td>
<td><p><strong>3</strong></p></td>
</tr>
<tr class="row-odd"><td><p>1</p></td>
<td><p>0.0278</p></td>
<td><p>0.649</p></td>
<td><p>0.668</p></td>
<td><p>0.652</p></td>
</tr>
<tr class="row-even"><td><p>2</p></td>
<td><p>0.0833</p></td>
<td><p>1.044</p></td>
<td><p>1.034</p></td>
<td><p>0.967</p></td>
</tr>
<tr class="row-odd"><td><p>3</p></td>
<td><p>0.1389</p></td>
<td><p>1.208</p></td>
<td><p>1.150</p></td>
<td><p>1.074</p></td>
</tr>
<tr class="row-even"><td><p>4</p></td>
<td><p>0.1944</p></td>
<td><p>1.215</p></td>
<td><p>1.094</p></td>
<td><p>1.103</p></td>
</tr>
<tr class="row-odd"><td><p>5</p></td>
<td><p>0.2500</p></td>
<td><p>1.214</p></td>
<td><p>1.053</p></td>
<td><p>1.108</p></td>
</tr>
<tr class="row-even"><td><p>6</p></td>
<td><p>0.3056</p></td>
<td><p>1.208</p></td>
<td><p>1.048</p></td>
<td><p>1.106</p></td>
</tr>
<tr class="row-odd"><td><p>7</p></td>
<td><p>0.3611</p></td>
<td><p>1.197</p></td>
<td><p>1.064</p></td>
<td><p>1.102</p></td>
</tr>
<tr class="row-even"><td><p>8</p></td>
<td><p>0.4167</p></td>
<td><p>1.189</p></td>
<td><p>1.095</p></td>
<td><p>1.097</p></td>
</tr>
<tr class="row-odd"><td><p>9</p></td>
<td><p>0.4722</p></td>
<td><p>1.188</p></td>
<td><p>1.121</p></td>
<td><p>1.094</p></td>
</tr>
<tr class="row-even"><td><p>10</p></td>
<td><p>0.5278</p></td>
<td><p>1.192</p></td>
<td><p>1.135</p></td>
<td><p>1.094</p></td>
</tr>
<tr class="row-odd"><td><p>11</p></td>
<td><p>0.5833</p></td>
<td><p>1.195</p></td>
<td><p>1.140</p></td>
<td><p>1.095</p></td>
</tr>
<tr class="row-even"><td><p>12</p></td>
<td><p>0.6389</p></td>
<td><p>1.190</p></td>
<td><p>1.138</p></td>
<td><p>1.096</p></td>
</tr>
<tr class="row-odd"><td><p>13</p></td>
<td><p>0.6944</p></td>
<td><p>1.156</p></td>
<td><p>1.130</p></td>
<td><p>1.095</p></td>
</tr>
<tr class="row-even"><td><p>14</p></td>
<td><p>0.7500</p></td>
<td><p>1.022</p></td>
<td><p>1.106</p></td>
<td><p>1.086</p></td>
</tr>
<tr class="row-odd"><td><p>15</p></td>
<td><p>0.8056</p></td>
<td><p>0.756</p></td>
<td><p>1.049</p></td>
<td><p>1.059</p></td>
</tr>
<tr class="row-even"><td><p>16</p></td>
<td><p>0.8611</p></td>
<td><p>0.614</p></td>
<td><p>0.933</p></td>
<td><p>0.971</p></td>
</tr>
<tr class="row-odd"><td><p>17</p></td>
<td><p>0.9167</p></td>
<td><p>0.481</p></td>
<td><p>0.669</p></td>
<td><p>0.738</p></td>
</tr>
<tr class="row-even"><td><p>18</p></td>
<td><p>0.9722</p></td>
<td><p>0.284</p></td>
<td><p>0.373</p></td>
<td><p>0.462</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="burnup-history-data">
<span id="id4"></span><h3>Burnup history data<a class="headerlink" href="#burnup-history-data" title="Permalink to this headline"></a></h3>
<p>The burnup history data block defines the irradiation history for the
assembly. These data are entered by keyword. The keywords are summarized
in <a class="reference internal" href="#tab2-3-6"><span class="std std-numref">Table 14</span></a>. Only the first four characters of the keywords are
required (i.e., any characters after the first four characters are
optional). A minimum of two entries are required for each cycle, (1) the
average assembly power (POWER=) and (2) the irradiation time (BURN=).
The decay time (DOWN=), if any, at the end of the cycle, and the number
of cross section libraries (NLIB=) are optional. The word END is
required to delimit the entries for each cycle. The entries within a
given cycle may be in any order.</p>
<p>The burnup history data block reading is initiated with the keywords
READ HISTORY (or BURNDATA) and terminated by END HISTORY (or BURNDATA).</p>
<p>POWER= The average specific power of the assembly for this cycle.
The units of the specific power are in MW/MTU (W/g) of initial uranium.
The axial and horizontal profiles are multiplied by the specific power
to achieve the desired spatially-dependent burnup profiles for the
assembly when FIX=NO (default). If FIX=YES, the specific power input
using this keyword is assumed to be uniform over all fuel regions (axial
and horizontal) and the code will adjust the irradiation time to obtain
the desired burnup for each region.</p>
<p>BURN= THE IRRADIATION TIME FOR THIS CYCLE. The cycle irradiation time in
days.</p>
<p>DOWN= CYCLE DOWN TIME. An optional entry to specify the down time, in
days, at the end of an irradiation cycle. The down time is simulated as
an irradiation time step of effectively zero power after the irradiation
cycle. The down time for the last cycle is simulated as a separate
ORIGEN decay case with nine equally-spaced time steps. If a negative
down time is input, the time steps are spaced logarithmically.</p>
<p>NLIB= LIBRARIES PER CYCLE. An optional entry to request multiple cross
section libraries during a depletion cycle. If requested, the code
automatically subdivides the cycle in NLIB segments of uniform duration
and generates a separate library for the depletion analysis for each
segment using ARP. Generating multiple libraries provides a more
accurate representation of the time-dependent cross section variation
during the burnup analysis. Each segment of the cycle is assumed to have
the same specific power, and no down time is assumed between each
segment of the cycle.</p>
<p>END The word END is required to terminate the input for each cycle.</p>
<p>Repeat the above entries for each cycle to define the complete assembly
power history.</p>
<span id="tab2-3-6"></span><table class="docutils align-center" id="id16">
<caption><span class="caption-number">Table 14 </span><span class="caption-text">Table of power history data.</span><a class="headerlink" href="#id16" 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>
<tbody>
<tr class="row-odd"><td><p><strong>Keyword</strong></p>
<p><strong>name</strong></p>
</td>
<td><p><strong>Data</strong></p>
<p><strong>type</strong></p>
</td>
<td><p><strong>Default</strong></p>
<p><strong>value</strong></p>
</td>
<td><p><strong>Comments</strong></p></td>
</tr>
<tr class="row-even"><td><p>READ HISTORY
(or BURNDATA)<sup>a</sup></p></td>
<td></td>
<td></td>
<td><p>Start of burnup
history data
block</p></td>
</tr>
<tr class="row-odd"><td><p>POWER=</p></td>
<td><p>Real variable</p></td>
<td><p>None</p></td>
<td><p>Average
assembly power
for this cycle
(MW/MTU)</p></td>
</tr>
<tr class="row-even"><td><p>BURN=</p></td>
<td><p>Real variable</p></td>
<td><p>None</p></td>
<td><p>Cycle
irradiation
time (days)</p></td>
</tr>
<tr class="row-odd"><td><p>DOWN=</p></td>
<td><p>Real variable</p></td>
<td><p>0</p></td>
<td><p>End-of-cycle
decay time
(days).
Optional. A
negative down
time may be
used to select
logarithmic
decay time
intervals for
the last decay
case.</p></td>
</tr>
<tr class="row-even"><td><p>NLIB/CYCLE=</p></td>
<td><p>Integer
variable</p></td>
<td><p>1</p></td>
<td><p>Number of
libraries to be
applied in this
cycle.
Optional.
If multiple
libraries are
requested for
this cycle, the
cycle is
subdivided into
equal time
segments, and
an updated
library is
generated for
each segment.
No down time is
simulated
between
segments.</p></td>
</tr>
<tr class="row-odd"><td><p>END</p></td>
<td></td>
<td></td>
<td><p>Required.
Defines the end
of the data for
the current
cycle. Repeat
the above
entries for
each cycle in
the irradiation
history. An
END, not to
begin in
column 1, must
terminate each
cycle
definition.</p></td>
</tr>
<tr class="row-even"><td><p>END HISTORY (or
BURNDATA)<em>a</em></p></td>
<td></td>
<td></td>
<td><p>End block</p></td>
</tr>
<tr class="row-odd"><td><p><sup>a</sup> Only
the first four
characters are
required, i.e.,
HIST (or BURN).</p></td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="search-parameter-data">
<h3>Search parameter data<a class="headerlink" href="#search-parameter-data" title="Permalink to this headline"></a></h3>
<p>The search parameter data block defines input data for burnup loading
curve analyses for commercial UO<sub>2</sub> spent fuels. Burnup history
input data are not allowed in an input file that supplies search
parameters. A burnup history data block is generated in STARBUCS for
subsequent iterative calculations using the initial user-supplied search
parameter data. STARBUCS sample problem <em>starbucs1.input</em> contains a
search data block to request burnup loading curve analyses for spent
fuel at various burnups. The search data block reading is initiated with
the keywords READ SEARCH and terminated by END SEARCH. The keywords are
summarized in <a class="reference internal" href="#tab2-3-7"><span class="std std-numref">Table 15</span></a>. These keywords may be in any order.</p>
<p>USL= THE UPPER SUBCRITICAL LIMIT FOR BURNUP LOADING.</p>
<p>EPS= TOLERANCE ON CONVERGENCE. The convergence criterion used in the
search for initial fuel enrichment so that user-specified <em>k</em><sub>eff</sub> value
is within USL ± EPS. The tolerance value must be greater that the
standard deviation of the calculated k<sub>eff</sub> for the solution to
converge.</p>
<p>ITMAX= MAXIMUM ITERATIONS ALLOWED FOR EACH ENRICHMENT SEARCH. The search
for initial fuel enrichment stops when the number of iterations exceeds
this parameter and a warning message is provided to the user.</p>
<p>ECL= LOWER ENRICHMENT CONSTRAINT. The unit for this parameter is wt%
<sup>235</sup>U. The lower enrichment constraint must be within the
enrichment interval used in the ORIGEN library specified in READ CONTROL
data block.</p>
<p>ECH= UPPER ENRICHMENT CONSTRAINT. The unit for this parameter is wt%
<sup>235</sup>U. The upper enrichment constraint must be within the
enrichment interval used in the ORIGEN library specified in READ CONTROL
data block.</p>
<p>BU= ARRAY OF REQUESTED BURNUP VALUES (GWd/MTU). The word END is required
to terminate this array. The user inputs a series of discharge burnup
values for which the initial fuel enrichments that result in a desired
<em>k</em><sub>eff</sub> value (USL ± EPS) are to be determined.</p>
<p>AVGBU= AVERAGE BURNUP PER CYCLE (GWd/MTU). An optional entry used to
determine the number of irradiation cycles as the ratio of a burnup
value in the BU array to AVGBU.</p>
<p>POWER= The average specific power of the assembly. The units of the
specific power are in MW/MTU (W/g) of initial uranium. This entry has
the same function as the entry for POWER= keyword in the HISTORY data
block (see <a class="reference internal" href="#burnup-history-data"><span class="std std-ref">Burnup history data</span></a>). It is also used to determine cycle
irradiation time as the ratio of a burnup value in the BU array to
average assembly power.</p>
<p>FDT= FRACTIONAL DOWNTIME. An optional entry used to determine down time
between irradiation cycles (the entry for DOWN= keyword in the HISTORY
data block) if fuel irradiation requires two or more cycles. For
example, for a cycle with 365 days of irradiation followed by a 30-day
downtime, FDT = 30 / 395 = 0.07595. STARBUCS uses the user-provided FDT
to compute cycle downtime as the irradiation time per cycle multiplied
by FDT and divided by (1-FDT).</p>
<p>DEC= DECAY TIME AFTER IRRADIATION. An optional entry to specify the
decay time, in days, after fuel discharge. A negative value may be used
to select logarithmic decay time intervals.</p>
<p>NLIB= NUMBER OF LIBRARIES PER CYCLE. An optional entry to request
multiple cross section libraries during a depletion cycle. Generating
multiple libraries provides a more accurate representation of the
time-dependent cross section variation during the burnup analysis. Each
segment of the cycle is assumed to have the same specific power.</p>
<p>FFE= FRESH FUEL ENRICHMENT. The purpose of this option is to help in
reducing the total number of iterations needed to achieve convergence.
There are two options implemented in STARBUCS for the fresh fuel
enrichment value to be used in the first inner iterations over fuel
enrichment, FFE=SEARCH (default) and FFE=INPUT. With the default option
(FFE=SEARCH), the lower enrichment bound and the starting fresh fuel
enrichment at the beginning of a search are adjusted based on the
results of the previous outer iteration over burnup. The procedure
includes the following steps. First, the user requested burnup values
are sorted in ascending order so that STARBUCS outer iterations over
burnup proceed from the lowest to the highest burnup value. Then, the
initial fresh fuel for the lowest burnup is changed to the mid-value of
the enrichment interval, (ECL+ECU)/2, and the search for the fresh fuel
enrichment corresponding to the lowest burnup is initiated and
completed. Suppose that a solution for this burnup step exists. This
solution becomes the lower enrichment constraint (ECL) in the search
passes for the next burnup value and the initial fresh fuel enrichment
is chosen as the middle point of the enrichment interval. The procedure
is applied for the entire set of the requested burnups. The average
number of iterations for each burnup step with this option is
approximately 4. The alternate option (FFE=INPUT) starts a search for
fuel enrichment with the user supplied fresh fuel enrichment.</p>
<span id="tab2-3-7"></span><table class="docutils align-center" id="id17">
<caption><span class="caption-number">Table 15 </span><span class="caption-text">Table of search data.</span><a class="headerlink" href="#id17" 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>
<tbody>
<tr class="row-odd"><td><p><strong>Keyword</strong></p>
<p><strong>Name</strong></p>
</td>
<td><p><strong>Data</strong></p>
<p><strong>type</strong></p>
</td>
<td><p><strong>Default</strong></p>
<p><strong>value</strong></p>
</td>
<td><p><strong>Comments</strong></p></td>
</tr>
<tr class="row-even"><td><p>READ SEARCH<sup>a</sup></p></td>
<td></td>
<td></td>
<td><p>Initiate
reading the
search block of
data.</p></td>
</tr>
<tr class="row-odd"><td><p>USL=</p></td>
<td><p>Real</p></td>
<td><p>1.0</p></td>
<td><p>Upper
subcritical
limit.</p></td>
</tr>
<tr class="row-even"><td><p>EPS=</p></td>
<td><p>Real</p></td>
<td><p>0.005</p></td>
<td><p>Tolerance on
convergence.</p></td>
</tr>
<tr class="row-odd"><td><p>ITMAX=</p></td>
<td><p>Integer</p></td>
<td><p>10</p></td>
<td><p>Iteration
limit.</p></td>
</tr>
<tr class="row-even"><td><p>ECL=</p></td>
<td><p>Real</p></td>
<td><p>1.5</p></td>
<td><p>Lower initial
fuel enrichment
constraint
(U-235 wt%).</p></td>
</tr>
<tr class="row-odd"><td><p>ECH=</p></td>
<td><p>Real</p></td>
<td><p>5.0</p></td>
<td><p>Upper initial
fuel enrichment
constraint
(U-235 wt%).</p></td>
</tr>
<tr class="row-even"><td><p>BU</p></td>
<td><p>Real<sup>b</sup></p></td>
<td><p>None</p></td>
<td><p>Array entry of
requested
burnup values
(GWd/MTU).<sup>c</sup></p></td>
</tr>
<tr class="row-odd"><td><p>AVGBU=</p></td>
<td><p>Real</p></td>
<td><p>20.0</p></td>
<td><p>Average burnup
per cycle.</p></td>
</tr>
<tr class="row-even"><td><p>POWER=</p></td>
<td><p>Real</p></td>
<td><p>25.0</p></td>
<td><p>Average
specific power
(W/g).</p></td>
</tr>
<tr class="row-odd"><td><p>FDT=</p></td>
<td><p>Real</p></td>
<td><p>0.2</p></td>
<td><p>Fractional
downtime.</p></td>
</tr>
<tr class="row-even"><td><p>DEC=</p></td>
<td><p>Real</p></td>
<td><p>1825.0</p></td>
<td><p>Decay time
(days).</p></td>
</tr>
<tr class="row-odd"><td><p>NLIB=</p></td>
<td><p>Integer</p></td>
<td><p>2</p></td>
<td><p>Libraries per
cycle.</p></td>
</tr>
<tr class="row-even"><td><p>FFE=</p></td>
<td><p>Character</p></td>
<td><p>SEARCH</p></td>
<td><p>Fresh fuel
option.
FFE=INPUT
starts the
outer
iterations over
the burnup
values with
user supplied
fresh fuel
composition.
FFE=SEARCH
helps in
reducing the
number of
search passes
(approximately
4 in average).</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p>END SEARCH</p></td>
<td></td>
<td><p>End of the
search data</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p><sup>a</sup> Only
the first four
characters are
required.</p>
<p><sup>b</sup> Terminate array data
entries with
end. Do not
place this end
in column 1.</p>
<p><sup>c</sup> There
are no restraints on the maximum number of the
burnup values
requested in
burnup loading
curve
calculations. A
user may
consider
computer time
and resources
in assessing
the maximum
number of
burnup values
in this array.</p>
</td>
<td></td>
<td></td>
<td></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="keno-input-data">
<h3>KENO input data<a class="headerlink" href="#keno-input-data" title="Permalink to this headline"></a></h3>
<p>The KENO input for the problem is specified in the KENO data block.
Input to the data block is initiated with the data block keywords <strong>READ
KENO or READ KENOVA</strong> and is terminated by the keywords <strong>END</strong> <strong>KENO</strong>
or <strong>END</strong> <strong>KENOVA</strong> for criticality calculations using <strong>KENO V.a</strong>.
Input to the data block is initiated with the data block keywords <strong>READ
KENOVI or READ KENO6</strong> and is terminated by the keywords <strong>END</strong>
<strong>KENOVI</strong> or <strong>END</strong> <strong>KENO6</strong> for criticality calculations using
<strong>KENO VI</strong>. STARBUCS performs no error checking of the KENO input. The
data within the data block delimiters is copied, without change, to the
CSAS input file and executed. The user is therefore advised to ensure
that the KENO input is free of errors by first running the case within
CSAS5 or CSAS6 before applying the input in STARBUCS.</p>
<p>The input requirements for KENO V.a and KENO-VI are not described in
this section, but are described in detail in the KENO chapter of this
manual. This section describes only the input requirements as related to
the execution of KENO within STARBUCS and the conventions used for
module compatibility.</p>
<p>The mixture numbers for each of the non-fuel materials applied to the
material regions of the KENO model are defined as the mixture numbers
(MX) specified in the standard composition input. STARBUCS automatically
defines the <em>MIXTURE ID</em> for each of the fuel regions according to the
axial and/or horizontal zones defined by the NAX and NHZ entries in the
burnup-profile arrays. The first axial-zone mixture is assigned MX=101,
and is incremented by one for each additional axial zone. Therefore, in
a problem that defines 18 axial zones, spent fuel mixtures will be
generated with identifiers that range from 101 to 118. The
correspondence of these mixtures to the assembly locations is determined
by the ordering of the AXP= input array that defines the axial-burnup
profile for the assembly. If the AXP= array orders the burnup profile
from the bottom of the assembly to the top of the assembly, the
resulting MX=101 will correspond to the bottom axial-zone segment, and
MX=118 would correspond to the top axial zone. If multiple horizontal
zones are defined, then the numbering sequence of the second horizontal
zone will start at MX=201 and, in the example given here, would range up
to MX=218. Refer to <a class="reference internal" href="#cap-and-lim"><span class="std std-ref">Capabilities and Limitations</span></a> for limitations in the mixture-numbering
scheme. The mixture-numbering scheme is illustrated in <a class="reference internal" href="#fig2-3-3"><span class="std std-numref">Fig. 19</span></a>.</p>
</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>A series of example problems are presented to illustrate the application
of STARBUCS to burnup-credit criticality safety and burnup loading curve
analyses. Sample problem 1 is a simple pin-cell problem for burnup
loading curve iterative calculations. The fuel pin contains a single
axial-burnup zone (i.e., uniform-axial burnup). It is useful to
illustrate the main features of the system and demonstrate functionality
of the system modules within SCALE. Problem 2 illustrates the same
problem with 18-axial burnup-dependent zones. Problem 3 extends the
pin-cell model to an array of spent fuel assemblies residing in a
water-filled pool. The models apply 18-axial-burnup-dependent zones.
Problem 4 is a generic cask model, and this problem exercises more of
the burnup credit options available in STARBUCS. Problem 5 illustrates
the use of the horizontal-burnup option for a simple 4 × 4 array of
spent fuel assemblies residing in water. Sample problem 6 uses KENO-VI
to model a hexagonal VVER‑440 fuel assembly.</p>
<div class="section" id="sample-problem-1">
<h3>Sample problem 1<a class="headerlink" href="#sample-problem-1" title="Permalink to this headline"></a></h3>
<p>Sample problem 1, listed in <a class="reference internal" href="#list2-3-1"><span class="std std-numref">Listing 1</span></a>, defines a simple infinite
UO<sub>2</sub> pin-cell model with uniform-axial burnup for burnup loading
curve calculations. The initial fuel enrichment is 2.0 wt %. The control
parameter data block specifies that the standard Westinghouse (W)
17 × 17 ORIGEN library is to be used for the depletion analysis. The
burnup-credit criticality calculation uses a subset of the major
actinides as defined in the NUC= array. The sample problem contains a
<em>read search</em>” data block, which provides an upper limit for
subcriticality, <em>usl</em>, a tolerance value for the search algorithm,
<em>eps</em>, the lower and upper enrichment bounds, <em>ecl</em> and e<em>ch</em>,
respectively, the maximum number of iterations for each burnup value
requested, <em>imaxl</em>, average specific power in W/g, <em>power</em>, decay time
after irradiation in days, <em>dec</em>, number of libraries per cycle, <em>nlib</em>,
average burnup per cycle in GWd/MTU, <em>avgbu</em>, fractional downtime,
<em>fdt</em>, and a set of burnup values, <em>bu</em> array.</p>
</div>
<div class="section" id="sample-problem-2">
<h3>Sample problem 2<a class="headerlink" href="#sample-problem-2" title="Permalink to this headline"></a></h3>
<p>Sample problem 2, listed in <a class="reference internal" href="#list2-3-2"><span class="std std-numref">Listing 2</span></a>, illustrates a simple pin-cell
model using 18-axial-burnup-dependent zones. In this example, the
built-in axial profiles for three burnup ranges are applied using the
NAX= −18 option (see profiles in <a class="reference internal" href="#tab2-3-5"><span class="std std-numref">Table 13</span></a>). STARBUCS determines the
average assembly burnup from the power history data input, and
automatically selects the appropriate profile based on the discharge
assembly burnup. The axial-profile data were developed for a predefined
axial-zoning structure (i.e., fraction of the assembly height). It is
important that the KENO V.a geometry model therefore also reflect this
axial-zone structure. That is, the height of each axial zone in the
criticality model must conform to the axial zones for the profile
applied in the analysis. In this example, the total pin height is
365.7 cm (144 in.), which is subdivided into 18 equal-height segments of
20.32 cm each.</p>
<p>The burnup-dependent cross sections generated for the criticality
analysis have material identifiers ranging from 101 (bottom) to
118 (top). There is no constraint on how the fuel materials can be
applied in the KENO V.a model. For example, the order of the material
numbers could easily be reversed, which would effectively invert the
profile and could be used to simulate an assembly loaded upside down. It
is also not necessary to use all of the materials in the problem. For
instance, all fuel regions in the KENO V.a model could be assigned the
same fuel mixture number to represent a flat axial profile having a
burnup value equal to that of the particular mixture used. The average
assembly burnup would also be equal to that of the particular mixture
used, and not that defined by the power history data block.</p>
<div class="literal-block-wrapper docutils container" id="list2-3-1">
<div class="code-block-caption"><span class="caption-number">Listing 1 </span><span class="caption-text">STARBUCS input listing for sample problem 1</span><a class="headerlink" href="#list2-3-1" title="Permalink to this code"></a></div>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span>    <span class="err">=starbucs</span>
   <span class="err">PWR</span> <span class="m">17</span><span class="err">x</span><span class="m">17</span> <span class="err">Fuel</span> <span class="err">Assembly</span> <span class="err">-</span> <span class="err">uniform</span> <span class="err">axial</span> <span class="err">burnup</span> <span class="err">rods</span>
  <span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
  <span class="n">read</span><span class="err"> </span><span class="n">comp</span>
  <span class="err">&#39;</span> <span class="err">UO</span><span class="m">2</span> <span class="err">Fuel</span> <span class="m">2</span><span class="err">.</span><span class="m">0</span> <span class="err">wt%</span> <span class="err">u-</span><span class="m">235</span>
   <span class="err">uo</span><span class="m">2</span>    <span class="m">1</span> <span class="err">den=</span><span class="m">10</span><span class="err">.</span><span class="m">96</span> <span class="m">0</span><span class="err">.</span><span class="m">95</span> <span class="m">293</span><span class="err">.</span><span class="m">0</span> <span class="m">92235</span> <span class="m">2</span><span class="err">.</span><span class="m">0</span> <span class="m">92238</span> <span class="m">98</span><span class="err">.</span><span class="m">0</span> <span class="n">end</span>
  <span class="err">&#39;Zircalloy</span>
   <span class="err">zirc</span><span class="m">4</span>  <span class="m">2</span>  <span class="m">1</span>  <span class="n">end</span>
  <span class="err">&#39;Water</span>
   <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">3</span>  <span class="m">1</span>  <span class="n">end</span>
  <span class="err">&#39;Gap</span>
   <span class="err">n</span> <span class="m">4</span> <span class="err">den=</span><span class="m">0</span><span class="err">.</span><span class="m">00125</span> <span class="m">1</span> <span class="n">end</span>
  <span class="n">end</span><span class="err"> </span><span class="n">comp</span>
  <span class="n">read</span><span class="err"> </span><span class="n">celldata</span>
   <span class="err">latticecell</span> <span class="err">squarepitch</span>  <span class="err">pitch=</span><span class="m">1</span><span class="err">.</span><span class="m">259</span> <span class="m">3</span> <span class="err">fueld=</span><span class="m">0</span><span class="err">.</span><span class="m">805</span> <span class="m">1</span> <span class="err">cladd=</span><span class="m">0</span><span class="err">.</span><span class="m">95</span> <span class="m">2</span> <span class="err">gapd=</span><span class="m">0</span><span class="err">.</span><span class="m">822</span> <span class="m">4</span> <span class="n">end</span>
  <span class="n">end</span><span class="err"> </span><span class="n">celldata</span>
  <span class="err">&#39;</span> <span class="err">Enter</span> <span class="err">burnup</span> <span class="err">credit</span> <span class="err">control</span> <span class="err">parameters</span>
  <span class="n">read</span><span class="err"> </span><span class="n">control</span>
   <span class="err">arp=w</span><span class="m">17</span><span class="err">x</span><span class="m">17</span>
   <span class="err">axp=</span> <span class="m">1</span> <span class="n">end</span>
   <span class="err">nuc=</span> <span class="err">u-</span><span class="m">234</span> <span class="err">u-</span><span class="m">235</span> <span class="err">u-</span><span class="m">236</span> <span class="err">u-</span><span class="m">238</span> <span class="err">pu-</span><span class="m">238</span> <span class="err">pu-</span><span class="m">239</span> <span class="err">pu-</span><span class="m">240</span>
        <span class="err">pu-</span><span class="m">241</span> <span class="err">pu-</span><span class="m">242</span> <span class="err">am-</span><span class="m">241</span> <span class="err">am-</span><span class="m">242</span><span class="err">m</span> <span class="err">am-</span><span class="m">243</span> <span class="err">np-</span><span class="m">237</span> <span class="n">end</span>
   <span class="err">fle=all</span>
  <span class="n">end</span><span class="err"> </span><span class="n">control</span>
  <span class="n">read</span><span class="err"> </span><span class="n">search</span>
    <span class="err">usl=</span><span class="m">0</span><span class="err">.</span><span class="m">96</span>
    <span class="err">eps=</span><span class="m">0</span><span class="err">.</span><span class="m">002</span>
    <span class="err">ecl=</span><span class="m">1</span><span class="err">.</span><span class="m">51</span>
    <span class="err">ech=</span><span class="m">4</span><span class="err">.</span><span class="m">99</span>
    <span class="err">itmax=</span><span class="m">10</span>
    <span class="err">power=</span><span class="m">60</span><span class="err">.</span><span class="m">0</span>
    <span class="err">dec=</span><span class="m">1826</span><span class="err">.</span><span class="m">25</span>
    <span class="err">nlib=</span><span class="m">2</span>
    <span class="err">avgbu=</span><span class="m">20</span>
    <span class="err">fdt=</span><span class="m">0</span><span class="err">.</span><span class="m">2</span>
    <span class="err">ffe=input</span>
    <span class="err">bu=</span> <span class="m">10</span> <span class="m">50</span> <span class="m">70</span>  <span class="n">end</span>
  <span class="n">end</span><span class="err"> </span><span class="n">search</span>
  <span class="n">read</span><span class="err"> </span><span class="n">kenova</span>
  <span class="err">&#39;</span> <span class="err">infinite</span> <span class="err">pin</span> <span class="err">cell</span> <span class="err">lattice</span>
  <span class="err">&#39;</span>
  <span class="err">&#39;**************************************</span>
  <span class="err">&#39;*</span> <span class="err">materials</span>
  <span class="err">&#39;*</span> <span class="m">101</span> <span class="err">=</span> <span class="err">uo</span><span class="m">2</span><span class="err">,</span> <span class="err">uniform</span> <span class="err">axial</span> <span class="err">region</span>
  <span class="err">&#39;*</span> <span class="m">2</span> <span class="err">=</span> <span class="err">Zircaloy</span>
  <span class="err">&#39;*</span> <span class="m">3</span> <span class="err">=</span> <span class="err">Water</span>
  <span class="err">&#39;*</span> <span class="m">4</span> <span class="err">=</span> <span class="err">Gap</span>
  <span class="err">&#39;**************************************</span>
  <span class="n">read</span><span class="err"> </span><span class="n">param</span><span class="err"> </span><span class="n">tme</span><span class="err">=10000 </span><span class="n">gen</span><span class="err">=510 </span><span class="n">nsk</span><span class="err">=10 </span><span class="n">npg</span><span class="err">=1000 </span><span class="n">end</span><span class="err"> </span><span class="n">param</span>
  <span class="n">read</span><span class="err"> </span><span class="n">geom</span>
  <span class="err">&#39;</span>           <span class="err">Fuel</span> <span class="err">Pin</span>
  <span class="err">global</span> <span class="err">unit</span> <span class="m">1</span>
   <span class="err">cylinder</span>   <span class="m">101</span>  <span class="m">1</span>   <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="m">50</span><span class="err">.</span><span class="m">0</span>  <span class="err">-</span><span class="m">50</span><span class="err">.</span><span class="m">0</span>
   <span class="err">cylinder</span>   <span class="m">4</span>    <span class="m">1</span>   <span class="m">0</span><span class="err">.</span><span class="m">4110</span>  <span class="m">50</span><span class="err">.</span><span class="m">0</span>  <span class="err">-</span><span class="m">50</span><span class="err">.</span><span class="m">0</span>
   <span class="err">cylinder</span>   <span class="m">2</span>    <span class="m">1</span>   <span class="m">0</span><span class="err">.</span><span class="m">4750</span>  <span class="m">50</span><span class="err">.</span><span class="m">0</span>  <span class="err">-</span><span class="m">50</span><span class="err">.</span><span class="m">0</span>
   <span class="err">cuboid</span>     <span class="m">3</span>    <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">0</span><span class="err">.</span><span class="m">6295</span>  <span class="m">50</span><span class="err">.</span><span class="m">0</span>  <span class="err">-</span><span class="m">50</span><span class="err">.</span><span class="m">0</span>
  <span class="err">&#39;</span>
  <span class="n">end</span><span class="err"> </span><span class="n">geom</span>
  <span class="n">read</span><span class="err"> </span><span class="n">bounds</span><span class="err">  </span><span class="n">all</span><span class="err">=</span><span class="n">reflect</span><span class="err">  </span><span class="n">end</span><span class="err"> </span><span class="n">bounds</span>
  <span class="n">end</span><span class="err"> </span><span class="n">data</span>
  <span class="n">end</span><span class="err"> </span><span class="n">kenova</span>
  <span class="n">end</span>
</pre></div>
</div>
</div>
<div class="literal-block-wrapper docutils container" id="list2-3-2">
<div class="code-block-caption"><span class="caption-number">Listing 2 </span><span class="caption-text">STARBUCS input listing for sample problem 2</span><a class="headerlink" href="#list2-3-2" title="Permalink to this code"></a></div>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span><span class="nf">=starbucs</span>
 <span class="err">PWR</span> <span class="m">17</span><span class="err">x</span><span class="m">17</span> <span class="err">Fuel</span> <span class="err">Assembly</span> <span class="err">-</span> <span class="m">18</span><span class="err">-zone</span> <span class="err">axial</span> <span class="err">burnup</span> <span class="err">profile</span>
<span class="err">v</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">comp</span>
<span class="c">&#39; UO2 Fuel 2.0 wt% u-235</span>
 <span class="err">uo</span><span class="m">2</span>    <span class="m">1</span> <span class="err">den=</span><span class="m">10</span><span class="err">.</span><span class="m">96</span> <span class="m">0</span><span class="err">.</span><span class="m">95</span> <span class="m">293</span><span class="err">.</span><span class="m">0</span> <span class="m">92235</span> <span class="m">2</span><span class="err">.</span><span class="m">0</span> <span class="m">92238</span> <span class="m">98</span><span class="err">.</span><span class="m">0</span> <span class="n">end</span>
<span class="c">&#39;Zircalloy</span>
 <span class="err">zirc</span><span class="m">4</span>  <span class="m">2</span>  <span class="m">1</span>  <span class="n">end</span>
<span class="c">&#39;Water</span>
 <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">3</span>  <span class="m">1</span>  <span class="n">end</span>
<span class="c">&#39;Gap</span>
 <span class="err">n</span> <span class="m">4</span> <span class="err">den=</span><span class="m">0</span><span class="err">.</span><span class="m">00125</span> <span class="m">1</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">comp</span>
<span class="n">read</span><span class="err"> </span><span class="n">celldata</span>
 <span class="err">latticecell</span> <span class="err">squarepitch</span>  <span class="err">pitch=</span><span class="m">1</span><span class="err">.</span><span class="m">259</span> <span class="m">3</span> <span class="err">fueld=</span><span class="m">0</span><span class="err">.</span><span class="m">805</span> <span class="m">1</span> <span class="err">cladd=</span><span class="m">0</span><span class="err">.</span><span class="m">95</span> <span class="m">2</span> <span class="err">gapd=</span><span class="m">0</span><span class="err">.</span><span class="m">822</span> <span class="m">4</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">celldata</span>
<span class="c">&#39; Enter burnup credit control parameters</span>
<span class="n">read</span><span class="err"> </span><span class="n">control</span>
<span class="err">arp=w</span><span class="m">17</span><span class="err">x</span><span class="m">17</span>  <span class="err">nax=-</span><span class="m">18</span>
<span class="err">nuc=</span> <span class="err">u-</span><span class="m">234</span> <span class="err">u-</span><span class="m">235</span> <span class="err">u-</span><span class="m">236</span> <span class="err">u-</span><span class="m">238</span> <span class="err">pu-</span><span class="m">238</span> <span class="err">pu-</span><span class="m">240</span>
    <span class="err">pu-</span><span class="m">241</span> <span class="err">pu-</span><span class="m">242</span> <span class="err">am-</span><span class="m">241</span> <span class="err">am-</span><span class="m">242</span><span class="err">m</span> <span class="err">am-</span><span class="m">243</span> <span class="err">np-</span><span class="m">237</span> <span class="n">end</span>
<span class="err">fle=o-</span><span class="m">16</span> <span class="err">h-</span><span class="m">1</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">control</span>
<span class="n">read</span><span class="err"> </span><span class="n">hist</span>
  <span class="err">power=</span><span class="m">35</span><span class="err">.</span><span class="m">001</span> <span class="err">burn=</span><span class="m">100</span> <span class="err">nlib=</span><span class="m">1</span> <span class="n">end</span>
  <span class="err">power=</span><span class="m">28</span><span class="err">.</span><span class="m">5</span>   <span class="err">burn=</span><span class="m">230</span> <span class="err">down=</span><span class="m">100</span> <span class="err">nlib=</span><span class="m">2</span> <span class="n">end</span>
  <span class="err">power=</span><span class="m">24</span><span class="err">.</span><span class="m">001</span> <span class="err">burn=</span><span class="m">300</span> <span class="err">nlib=</span><span class="m">2</span> <span class="err">down=</span><span class="m">1826</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">hist</span>
<span class="n">read</span><span class="err"> </span><span class="n">kenova</span>
<span class="c">&#39;**************************************</span>
<span class="c">&#39;* materials</span>
<span class="c">&#39;* 101-118 = uo2, 18-axial zone model</span>
<span class="c">&#39;* 2 = Zircaloy</span>
<span class="c">&#39;* 3 = Water</span>
<span class="c">&#39;* 4 = Gap</span>
<span class="c">&#39;**************************************</span>
<span class="n">read</span><span class="err"> </span><span class="n">param</span><span class="err">  </span><span class="n">tme</span><span class="err">=10000 </span><span class="n">gen</span><span class="err">=510 </span><span class="n">nsk</span><span class="err">=10 </span><span class="n">npg</span><span class="err">=1000 </span><span class="n">end</span><span class="err"> </span><span class="n">param</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
<span class="c">&#39;           Fuel Pin</span>
<span class="err">global</span> <span class="err">unit</span> <span class="m">1</span>
 <span class="err">cylinder</span>   <span class="m">101</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span> <span class="err">-</span><span class="m">162</span><span class="err">.</span><span class="m">53</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">102</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span> <span class="err">-</span><span class="m">142</span><span class="err">.</span><span class="m">22</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">103</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span> <span class="err">-</span><span class="m">121</span><span class="err">.</span><span class="m">90</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">104</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span> <span class="err">-</span><span class="m">101</span><span class="err">.</span><span class="m">58</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">105</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="err">-</span><span class="m">81</span><span class="err">.</span><span class="m">27</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">106</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="err">-</span><span class="m">60</span><span class="err">.</span><span class="m">95</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">107</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="err">-</span><span class="m">40</span><span class="err">.</span><span class="m">63</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">108</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="err">-</span><span class="m">20</span><span class="err">.</span><span class="m">32</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">109</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>    <span class="m">0</span><span class="err">.</span><span class="m">00</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">110</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>   <span class="m">20</span><span class="err">.</span><span class="m">32</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">111</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>   <span class="m">40</span><span class="err">.</span><span class="m">63</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">112</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>   <span class="m">60</span><span class="err">.</span><span class="m">95</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">113</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>   <span class="m">81</span><span class="err">.</span><span class="m">27</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">114</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="m">101</span><span class="err">.</span><span class="m">58</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">115</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="m">121</span><span class="err">.</span><span class="m">90</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">116</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="m">142</span><span class="err">.</span><span class="m">22</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">117</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="m">162</span><span class="err">.</span><span class="m">53</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">118</span>  <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4025</span>  <span class="m">182</span><span class="err">.</span><span class="m">85</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">4</span>    <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4110</span>  <span class="m">182</span><span class="err">.</span><span class="m">85</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cylinder</span>   <span class="m">2</span>    <span class="m">1</span>  <span class="m">0</span><span class="err">.</span><span class="m">4750</span>  <span class="m">182</span><span class="err">.</span><span class="m">85</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
 <span class="err">cuboid</span>     <span class="m">3</span>    <span class="m">1</span> <span class="m">4</span><span class="err">p</span><span class="m">0</span><span class="err">.</span><span class="m">6295</span> <span class="m">182</span><span class="err">.</span><span class="m">85</span>  <span class="err">-</span><span class="m">182</span><span class="err">.</span><span class="m">85</span>
<span class="c">&#39;</span>
<span class="n">end</span><span class="err"> </span><span class="n">geom</span>
<span class="n">read</span><span class="err"> </span><span class="n">bounds</span><span class="err">  </span><span class="n">all</span><span class="err">=</span><span class="n">reflect</span><span class="err">  </span><span class="n">end</span><span class="err"> </span><span class="n">bounds</span>
<span class="n">end</span><span class="err"> </span><span class="n">data</span>
<span class="n">end</span><span class="err"> </span><span class="n">kenova</span>
<span class="n">end</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="sample-problem-3">
<h3>Sample problem 3<a class="headerlink" href="#sample-problem-3" title="Permalink to this headline"></a></h3>
<p>Sample problem 3, listed in <a class="reference internal" href="#list2-3-3"><span class="std std-numref">Listing 3</span></a>, performs a burnup-credit
criticality safety calculation using the SCALE 238-group ENDF/B-VII
cross section library (V7-238) for an array of Combustion Engineering
(CE) 14 × 14 spent fuel assemblies in water. A subset of burnup-credit
actinides and fission products are included in the criticality
calculation. A user-supplied 18-axial-region-burnup profile of the
assemblies is input. This profile was obtained from the
axial-burnup-profile database <a class="bibtex reference internal" href="#cacciapouti-axial-2000" id="id5">[Cac00]</a> for Maine Yankee assembly N863. Note
that the axial profile will be normalized automatically by the code
using NPR=yes (default). The normalization is performed such that the
average value of the profile values is unity (i.e., the sum of the
profile values is equal to the number of axial zones). The 3.3 wt %
enriched UO<sub>2</sub> fuel is assumed to achieve a discharge burnup of
37,626 MWd/MTU in three cycles of approximately 12.5 GWd/MTU per cycle
and a downtime per cycle of 80 days, followed by a cooling time of
5 years after discharge (1826 days). An average assembly power level of
32 MW/MTU is used for the depletion calculation. Two libraries per cycle
are requested during the depletion. Note that by increasing the number
of libraries generated per cycle, the cross sections used in the burnup
analysis are updated more frequently to reflect the changes that occur
with burnup. The nominal CE 14 × 14 assembly design specifications were
obtained from <a class="bibtex reference internal" href="#dehart-extension-1996" id="id6">[DH96]</a>. The assembly pitch in the criticality
calculations is 22.78 cm. A cross section view of the assembly geometry,
a 2 × 8 array of water reflected assemblies, is illustrated in
<a class="reference internal" href="#fig2-3-5"><span class="std std-numref">Fig. 21</span></a>.</p>
<div class="literal-block-wrapper docutils container" id="list2-3-3">
<div class="code-block-caption"><span class="caption-number">Listing 3 </span><span class="caption-text">STARBUCS input listing for sample problem</span><a class="headerlink" href="#list2-3-3" title="Permalink to this code"></a></div>
<div class="highlight-scale notranslate"><div class="highlight"><pre><span></span>  <span class="err">=starbucs</span>
<span class="err">CE</span> <span class="m">14</span><span class="err">x</span><span class="m">14</span> <span class="err">assembly</span> <span class="m">2</span> <span class="err">x</span> <span class="m">8</span> <span class="err">array</span>
<span class="err">V</span><span class="m">7</span><span class="err">-</span><span class="m">238</span>
<span class="n">read</span><span class="err"> </span><span class="n">comp</span>
<span class="c">&#39; UO2 Fuel 3.3 wt% u235</span>
<span class="err">uo</span><span class="m">2</span>  <span class="m">1</span> <span class="err">den=</span><span class="m">10</span><span class="err">.</span><span class="m">045</span> <span class="m">1</span> <span class="m">273</span> <span class="m">92234</span> <span class="m">0</span><span class="err">.</span><span class="m">0294</span> <span class="m">92235</span> <span class="m">3</span><span class="err">.</span><span class="m">3</span> <span class="m">92236</span> <span class="m">0</span><span class="err">.</span><span class="m">0152</span> <span class="m">92238</span> <span class="m">96</span><span class="err">.</span><span class="m">6554</span> <span class="n">end</span>
<span class="c">&#39;Zircalloy</span>
 <span class="err">zirc</span><span class="m">4</span> <span class="m">2</span>  <span class="m">1</span>  <span class="n">end</span>
<span class="c">&#39;Water</span>
 <span class="err">h</span><span class="m">2</span><span class="err">o</span>    <span class="m">3</span>  <span class="m">1</span>  <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">comp</span>
<span class="n">read</span><span class="err"> </span><span class="n">celldata</span>
 <span class="err">latticecell</span> <span class="err">squarepitch</span>  <span class="err">pitch=</span><span class="m">1</span><span class="err">.</span><span class="m">473</span> <span class="m">3</span> <span class="err">fueld=</span><span class="m">0</span><span class="err">.</span><span class="m">968</span> <span class="m">1</span>
                          <span class="err">cladd=</span><span class="m">1</span><span class="err">.</span><span class="m">118</span> <span class="m">2</span>  <span class="err">gapd=</span><span class="m">0</span><span class="err">.</span><span class="m">985</span> <span class="m">0</span>  <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">celldata</span>
<span class="n">read</span><span class="err"> </span><span class="n">control</span>
<span class="err">arp=ce</span><span class="m">14</span><span class="err">x</span><span class="m">14</span> <span class="err">nax=</span><span class="m">18</span>
<span class="err">axp=</span>
  <span class="m">0</span><span class="err">.</span><span class="m">67053</span> <span class="m">0</span><span class="err">.</span><span class="m">93322</span> <span class="m">1</span><span class="err">.</span><span class="m">02433</span> <span class="m">1</span><span class="err">.</span><span class="m">05329</span> <span class="m">1</span><span class="err">.</span><span class="m">06026</span> <span class="m">1</span><span class="err">.</span><span class="m">06185</span>
  <span class="m">1</span><span class="err">.</span><span class="m">06215</span> <span class="m">1</span><span class="err">.</span><span class="m">06249</span> <span class="m">1</span><span class="err">.</span><span class="m">06312</span> <span class="m">1</span><span class="err">.</span><span class="m">06408</span> <span class="m">1</span><span class="err">.</span><span class="m">06541</span> <span class="m">1</span><span class="err">.</span><span class="m">06702</span>
  <span class="m">1</span><span class="err">.</span><span class="m">06836</span> <span class="m">1</span><span class="err">.</span><span class="m">06760</span> <span class="m">1</span><span class="err">.</span><span class="m">05918</span> <span class="m">1</span><span class="err">.</span><span class="m">02515</span> <span class="m">0</span><span class="err">.</span><span class="m">92262</span> <span class="m">0</span><span class="err">.</span><span class="m">66935</span> <span class="n">end</span>
<span class="err">nuc=</span>
  <span class="err">u-</span><span class="m">234</span>  <span class="err">u-</span><span class="m">235</span>  <span class="err">u-</span><span class="m">236</span>  <span class="err">u-</span><span class="m">238</span>  <span class="err">pu-</span><span class="m">238</span> <span class="err">pu-</span><span class="m">239</span> <span class="err">pu-</span><span class="m">240</span>
  <span class="err">pu-</span><span class="m">241</span> <span class="err">pu-</span><span class="m">242</span> <span class="err">am-</span><span class="m">241</span> <span class="err">np-</span><span class="m">237</span>
  <span class="err">mo-</span><span class="m">95</span>  <span class="err">tc-</span><span class="m">99</span>  <span class="err">ru-</span><span class="m">101</span> <span class="err">rh-</span><span class="m">103</span> <span class="err">ag-</span><span class="m">109</span> <span class="err">cs-</span><span class="m">133</span> <span class="err">nd-</span><span class="m">143</span>
  <span class="err">nd-</span><span class="m">145</span> <span class="err">sm-</span><span class="m">147</span> <span class="err">sm-</span><span class="m">149</span> <span class="err">sm-</span><span class="m">150</span> <span class="err">sm-</span><span class="m">151</span> <span class="err">eu-</span><span class="m">151</span> <span class="err">sm-</span><span class="m">152</span>
  <span class="err">eu-</span><span class="m">153</span> <span class="err">gd-</span><span class="m">155</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">control</span>
<span class="n">read</span><span class="err"> </span><span class="n">hist</span>
  <span class="err">power=</span><span class="m">32</span><span class="err">.</span><span class="m">00</span>  <span class="err">burn=</span><span class="m">391</span><span class="err">.</span><span class="m">937</span> <span class="err">nlib=</span><span class="m">2</span> <span class="err">down=</span><span class="m">80</span>  <span class="n">end</span>
  <span class="err">power=</span><span class="m">32</span><span class="err">.</span><span class="m">00</span>  <span class="err">burn=</span><span class="m">391</span><span class="err">.</span><span class="m">937</span> <span class="err">nlib=</span><span class="m">2</span> <span class="err">down=</span><span class="m">80</span>  <span class="n">end</span>
  <span class="err">power=</span><span class="m">32</span><span class="err">.</span><span class="m">00</span>  <span class="err">burn=</span><span class="m">391</span><span class="err">.</span><span class="m">937</span> <span class="err">nlib=</span><span class="m">2</span> <span class="err">down=</span><span class="m">1826</span> <span class="n">end</span>
<span class="n">end</span><span class="err"> </span><span class="n">hist</span>
<span class="n">read</span><span class="err"> </span><span class="n">keno</span>
<span class="c">&#39;</span>
<span class="c">&#39;******************************************</span>
<span class="c">&#39;* materials</span>
<span class="c">&#39;* 101 = uo2, lower axial region (0.67053)</span>
<span class="c">&#39;* 118 = uo2, upper axial region (0.66935)</span>
<span class="c">&#39;* 2 = Zircaloy</span>
<span class="c">&#39;* 3 = Water</span>
<span class="c">&#39;******************************************</span>
<span class="n">read</span><span class="err"> </span><span class="n">param</span>
 <span class="err">tme=</span><span class="m">10000</span> <span class="err">gen=</span><span class="m">510</span> <span class="err">nsk=</span><span class="m">10</span> <span class="err">npg=</span><span class="m">1000</span>
<span class="n">end</span><span class="err"> </span><span class="n">param</span>
<span class="n">read</span><span class="err"> </span><span class="n">geom</span>
<span class="c">&#39;  Fuel Pin</span>
<span class="err">unit</span>           <span class="m">1