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diff --git a/doc/IGE335/Section3.05_auto.tex b/doc/IGE335/Section3.05_auto.tex new file mode 100644 index 0000000..4d13c84 --- /dev/null +++ b/doc/IGE335/Section3.05_auto.tex @@ -0,0 +1,262 @@ +\subsection{The {\tt AUTO:} module}\label{sect:AUTOData} + +The Autosecol self-shielding module in DRAGON, called {\tt AUTO:}, allows the +correction of the microscopic cross sections to take into account the +self-shielding effects related to the resonant isotopes.\cite{autosecol} + +\vskip 0.08cm + +{\sl Autolib data} is a fine-group representation of microscopic cross-section data for the resonant isotopes available in a +{\sl Draglib} or {\sl APOLIB-2} cross-section library. Each fine group in the Autolib has a lethargy width which is an integer multiple of an +{\sl elementary lethargy width}. Elastic slowing-down scattering is assumed for the resonant isotopes. + +Integrating the Livolant-Jeanpierre equation over a fine group $g$, the Autosecol equation is written +\begin{equation} +\bff(\Omega)\cdot\bff(\nabla)\varphi_g(\bff(r),\bff(\Omega))\,+\,\Sigma_g(\bff(r))\,\varphi_g(\bff(r),\bff(\Omega))\,=\,{1\over 4\pi} \left[ \Sigma_{{\rm s},g}^+(\bff(r)) \, + \,\sum_h \Sigma_{{\rm s},j,g \leftarrow h}^{*} \, \varphi_h(\bff(r)) {\Delta u_h\over \Delta u_g} \right] +\label{eq:auto1} +\end{equation} + +\noindent where the group integrated fine structure function is written +\begin{equation} +\varphi_g(\bff(r))={1\over \Delta u_g}\int_{u_{g-1}}^{u_g} du\, \varphi(\bff(r),u) +\label{eq:auto2} +\end{equation} + +\noindent and where the $+$ and $*$ subscripts identify non-resonant and resonant isotopes respectively. + +\vskip 0.08cm + +The {\sl Autosecol method} consists to solve the Livolant-Jeanpierre equation over the Autolib energy mesh using a solution +technique of the Boltzmann transport equation available in DRAGON.\cite{PIP2009} The Autosecol method +is an accurate self-shielding technique relying on the fine-group solution of an heterogeneous transport equation. This approach may require +substantial CPU resources in actual production cases. + +\vskip 0.08cm + +Resonant isotopes are identified as such by the \dusa{inrs} parameter, as defined in +\Sect{LIBData}. The Autosecol self-shielding module is based on the following models: + +\begin{itemize} +\item The Livolant-Jeanpierre flux factorization and approximations are used to +uncouple the self-shielding treatment from the main flux calculation; +\item The resonant cross sections are represented using {\sl Autolib data} +recovered by the \moc{LIB:} module. +\item Probability tables are used in the unresolved energy domain to randomly +sample cross-section data into the Autolib fine mesh. The keyword \moc{SUBG} {\sl must} be +set in module {\tt LIB:}. +\item The resonant fine structure values $\varphi_g(\bff(r))$ are obtained as a solution +of the Autosecol Eq.~(\ref{eq:auto1}) over the Autolib fine mesh; +\item The flux can be solved using collision probabilities, or using {\sl any} +flux solution technique for which a tracking module is available; +\item All resonant isotopes with the same \dusa{inrs} index (see Sect.~\ref{sect:descmix1}) +are computed simultanously; +\item The distributed self-shielded effect is automatically taken into account +if different mixture indices are assigned to different regions inside the +resonant part of the cell. The rim effect can be computed by dividing the fuel +into "onion rings" and by assigning different mixture indices to them. +\item A SPH (superhomog\'en\'eisation) equivalence is performed to correct the +self-shielded cross sections from the non-linear effects related to the +heterogeneity of the geometry. +\end{itemize} + +\vskip 0.2cm + +The general format of the data for this module is: + +\begin{DataStructure}{Structure \dstr{AUTO:}} +\dusa{MICLIB} \moc{:=} \moc{AUTO:} \dusa{MICLIB\_SG} $[$ \dusa{MICLIB} $]$ +\dusa{TRKNAM} $[$ \dusa{TRKFIL} $]$ \moc{::} \dstr{descauto} +\end{DataStructure} + +\noindent where + +\begin{ListeDeDescription}{mmmmmmmm} + +\item[\dusa{MICLIB}] {\tt character*12} name of the \dds{microlib} that will +contain the microscopic and macroscopic cross sections updated by the +self-shielding module. If +\dusa{MICLIB} appears on both LHS and RHS, it is updated; otherwise, +\dusa{MICLIB} is created. + +\item[\dusa{MICLIB\_SG}] {\tt character*12} name of the \dds{microlib} builded +by module \moc{LIB:} and containing probability table information for the unresolved +domain. + +\item[\dusa{TRKNAM}] {\tt character*12} name of the required \dds{tracking} +data structure. + +\item[\dusa{TRKFIL}] {\tt character*12} name of the sequential binary tracking +file used to store the tracks lengths. This file is given if and only if it was +required in the previous tracking module call (see \Sect{TRKData}). + +\item[\dstr{descauto}] structure describing the self-shielding options. + +\end{ListeDeDescription} + +\subsubsection{Data input for module {\tt AUTO:}}\label{sect:descauto} + +\begin{DataStructure}{Structure \dstr{descauto}} +$[$ \moc{EDIT} \dusa{iprint} $]$ \\ +$[$ \moc{GRMIN} \dusa{lgrmin} $]~~[$ \moc{GRMAX} \dusa{lgrmax} $]$~~ +$[$ \moc{PASS} \dusa{ipass} $]~~[~\{$ \moc{SPH} $|$ \moc{NOSP} $\}~]$~~$[$ $\{$ \moc{TRAN} $|$ \moc{NOTR} $\}$ $]$ \\ +$[$ $\{$ \moc{PIJ} $|$ \moc{ARM} $\}$ $]$ \\ +$[[$ \moc{DILU} \dusa{isot\_d} \dusa{dilut} $]]$ \\ +$[$ \moc{KERN} \dusa{ialter} $]~~[$ \moc{MAXT} \dusa{maxtra} $]$ \\ +$[$~\moc{SEED} \dusa{iseed}~$]$ \\ +$[$ \moc{CALC} \\ +~~~~$[[$ \moc{REGI} \dusa{suffix} $[[$ \dusa{isot} $\{$ \moc{ALL} $|$ +(\dusa{imix}(i),i=1,\dusa{nmix}) $\}$ $]]$ \\ +~~~~$]]$ \\ +\moc{ENDC} $]$ \\ +{\tt ;} +\end{DataStructure} + +\noindent where + +\begin{ListeDeDescription}{mmmmmmmm} + +\item[\moc{EDIT}] keyword used to modify the print level \dusa{iprint}. + +\item[\dusa{iprint}] index used to control the printing of this module. The +amount of output produced by this tracking module will vary substantially +depending on the print level specified. + +\item[\moc{GRMIN}] keyword to specify the minimum group number considered +during the self-shielding process. + +\item[\dusa{lgrmin}] first group number considered during the +self-shielding process. By default, \dusa{lgrmin} is set to the first group +number containing self-shielding data in the library. + +\item[\moc{GRMAX}] keyword to specify the maximum group number considered +during the self-shielding process. + +\item[\dusa{lgrmax}] last group number considered during the self-shielding +process. By default, \dusa{lgrmax} is set is set to the last group +number containing self-shielding data in the library. + +\item[\moc{PASS}] keyword to specify the number of outer iterations during +the self-shielding process. If all \dusa{inrs} indices are set to one in module \moc{LIB:}, +these iterations are not required. + +\item[\dusa{ipass}] the number of iterations. The default is \dusa{ipass} $=1$ if +\dusa{MICLIB} is created. + +\item[\moc{SPH}] keyword to activate the SPH equivalence scheme which +modifies the self-shielded averaged neutron fluxes in +heterogeneous geometries (default option). + +\item[\moc{NOSP}] keyword to deactivate the SPH equivalence scheme which +modifies the self-shielded averaged neutron fluxes in heterogeneous geometries. + +\item[\moc{TRAN}] keyword to activate the transport correction option for +self-shielding calculations (see \moc{CTRA} in \Sectand{MACData}{LIBData}). This +is the default option. + +\item[\moc{NOTR}] keyword to deactivate the transport correction option for +self-shielding calculations (see \moc{CTRA} in \Sectand{MACData}{LIBData}). + +\item[\moc{PIJ}] keyword to specify the use of complete collision +probabilities in the subgroup and SPH equivalence calculations of {\tt AUTO:}. +This is the default option for \moc{EXCELT:} and \moc{SYBILT:} trackings. +This option is not available for \moc{MCCGT:} trackings. + +\item[\moc{ARM}] keyword to specify the use of iterative flux techniques +in the subgroup and SPH equivalence calculations of {\tt AUTO:}. +This is the default option for \moc{MCCGT:} trackings. + +\item[\moc{DILU}] keyword to input an additional microscopic dilution value for a specific isotope. By default, no dilution +source other than $\Sigma_{{\rm s},g}^+(\bff(r))$ is used. + +\item[\dusa{isot\_d}] {\tt character*8} alias name of the specific isotope. + +\item[\dusa{dilut}] dilution value in barn. + +\item[\moc{KERN}] keyword to input the type of elastic slowing-down kernel. + +\item[\dusa{ialter}] integer value indicating the type: +$$ +\textsl{ialter} = \left\{ +\begin{array}{ll} +0 & \textrm{use exact elastic kernel} \\ +1 & \textrm{use an approximate kernel for the resonant isotopes.} +\end{array} \right. +$$ + +\item[\moc{MAXT}] keyword to input a maximum storage size for the slowing-down kernel values. + +\item[\dusa{maxtra}] integer value indicating the storage size. The default value is \dusa{maxtra} $=$ 10000. + +\item[\moc{SEED}] keyword used to set the initial seed integer for the random number generator used in +the unresolved energy domain. By default, the seed integer is set from the processor clock. + +\item[\dusa{iseed}] initial seed integer. + +\item[\moc{CALC}] keyword to activate the simplified self-shielding +approximation in which a single self-shielded isotope is shared by many +resonant mixtures. + +\item[\moc{REGI}] keyword to specify a set of isotopes and mixtures that +will be self-shielded together. All the self-shielded isotopes in this group +will share the same 4--digit suffix. + +\item[\dusa{suffix}] {\tt character*4} suffix for the isotope names in this +group + +\item[\dusa{isot}] {\tt character*8} alias name of a self-shielded isotope in this +group + +\item[\moc{ALL}] keyword to specify that a unique self-shielded isotope will be +made for the complete domain + +\item[\dusa{imix}] list of mixture indices that will share the same self-shielded +isotope + +\item[\dusa{nmix}] number of mixtures that will share the same self-shielded +isotope + +\item[\moc{ENDC}] end of \moc{CALC} data keyword + +\end{ListeDeDescription} + +\vskip 0.15cm + +Here is an example of the data structure corresponding to a production case where +only $^{238}$U is assumed to show distributed self-shielding effects: + +\begin{verbatim} +LIBRARY2 := AUTO: LIBRARY TRACK :: + CALC REGI W1 PU239 ALL + REGI W1 PU241 ALL + REGI W1 PU240 ALL + REGI W1 PU242 ALL + REGI W1 U235 ALL + REGI W1 U236 ALL + REGI W1 PU238 ALL + REGI W1 U234 ALL + REGI W1 AM241 ALL + REGI W1 NP237 ALL + REGI W1 ZRNAT ALL + REGI W1 U238 <<COMB0101>> <<COMB0201>> <<COMB0301>> + <<COMB0401>> <<COMB0501>> + REGI W2 U238 <<COMB0102>> <<COMB0202>> <<COMB0302>> + <<COMB0402>> <<COMB0502>> + REGI W3 U238 <<COMB0103>> <<COMB0203>> <<COMB0303>> + <<COMB0403>> <<COMB0503>> + REGI W4 U238 <<COMB0104>> <<COMB0204>> <<COMB0304>> + <<COMB0404>> <<COMB0504>> + REGI W5 U238 <<COMB0105>> <<COMB0205>> <<COMB0305>> + <<COMB0405>> <<COMB0505>> + REGI W6 U238 <<COMB0106>> <<COMB0206>> <<COMB0306>> + <<COMB0406>> <<COMB0506>> + ENDC ; +\end{verbatim} + +\vskip 0.15cm + +In this case, $^{238}$U is self-shielded within six distributed regions (labeled +{\tt W1} to {\tt W6}) and each of these regions are merging volumes belonging +to five different fuel rods. The mixture indices of the 30 resonant volumes belonging +to the fuel are CLE-2000 variables labeled {\tt <<COMB0101>>} to {\tt <<COMB0506>>}. + +\eject |