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diff --git a/doc/IGE351/SectDgeometry.tex b/doc/IGE351/SectDgeometry.tex new file mode 100644 index 0000000..4ec2c75 --- /dev/null +++ b/doc/IGE351/SectDgeometry.tex @@ -0,0 +1,539 @@ +\section{Contents of a +\dir{geometry} directory}\label{sect:geometrydir} + +The {\tt L\_GEOM} specification is used to store structured geometric data, i.e., data characterized by some regularity in space. Sub-geometries can be embedded at specific node positions to build a more complex geometry. The following regular geometries can be described with the {\tt L\_GEOM} specification: +\begin{itemize} +\item Cartesian geometries in 1D, 2D and 3D +\item Cylindrical geometries in 1D and 2D ($R-Z$ or $R-\theta$) +\item Spherical geometries in 1D +\item Hexagonal geometries in 2D/3D +\item Various types of cells in 2D/3D Cartesian or hexagonal geometry +\item Cells with clusters of fuel rods +\item Various synthetic geometries (Do-it-yourself Apollo1 assembly and double-heterogeneity). +\end{itemize} + +This directory contains a compact description of a geometry. + +\subsection{State vector content for the \dir{geometry} data structure}\label{sect:geometrystate} + +The dimensioning parameters for this data structure, which are stored in the state vector +$\mathcal{S}^{G}$, represent: + +\begin{itemize} +\item The type of of geometry $F_{t}=\mathcal{S}^{G}_{1}$ + +\begin{displaymath} +F_{t} = \left\{ +\begin{array}{rl} + 0 & \textrm{Virtual geometry}\\ + 1 & \textrm{Homogeneous geometry} \\ + 2 & \textrm{Cartesian 1-D geometry} \\ + 3 & \textrm{Tube 1-D geometry} \\ + 4 & \textrm{Sphere 1-D geometry} \\ + 5 & \textrm{Cartesian 2-D geometry} \\ + 6 & \textrm{Tube ($R$-$Z$) geometry} \\ + 7 & \textrm{Cartesian 3-D geometry} \\ + 8 & \textrm{Hexagonal 2-D geometry} \\ + 9 & \textrm{Hexagonal 3-D geometry} \\ +10 & \textrm{Tube ($R$-$X$) geometry} \\ +11 & \textrm{Tube ($R$-$Y$) geometry} \\ +12 & \textrm{hexagonal 2--D geometry with triangular mesh} \\ +13 & \textrm{$z$-directed hexagonal 3--D geometry with triangular mesh} \\ +15 & \textrm{Tube ($R$-$\theta$) 2-D geometry} \\ +16 & \textrm{Triangular 2-D geometry} \\ +17 & \textrm{Triangular 3-D geometry} \\ +20 & \textrm{Cartesian 2-D geometry with annular sub-mesh} \\ +21 & \textrm{Cartesian 3-D geometry with $x-$directed cylindrical sub-mesh} \\ +22 & \textrm{Cartesian 3-D geometry with $y-$directed cylindrical sub-mesh} \\ +23 & \textrm{Cartesian 3-D geometry with $z-$directed cylindrical sub-mesh} \\ +24 & \textrm{Hexagonal 2-D geometry with annular sub-mesh} \\ +25 & \textrm{Hexagonal 3-D geometry with $z-$directed cylindrical sub-mesh } \\ +30 & \textrm{Do-it-yourself geometry} \\ +\end{array} \right. +\end{displaymath} +\eject + +\item The number of annular or cylindric mesh intervals in the geometry $N_{r}=\mathcal{S}^{G}_{2}$ + +\item The number of $x-$directed mesh intervals, hexagon or triangles in the geometry $N_{x}=\mathcal{S}^{G}_{3}$ + +\item The number of $y-$directed mesh intervals in the geometry $N_{y}=\mathcal{S}^{G}_{4}$ + +\item The number of $z-$directed mesh intervals in the geometry $N_{z}=\mathcal{S}^{G}_{5}$ + +\item The total number of mesh intervals in the geometry $N_{k}=\mathcal{S}^{G}_{6}$ +\begin{itemize} +\item for $F_{t}=$0 or 1, $N_{k}=1$; +\item for $F_{t}=$2, 5 or 7, $N_{k}=\max(N_{x},1)\times \max(N_{y},1)\times \max(N_{z},1)$; +\item for $F_{t}=$3, 6, 10 or 11, $N_{k}=N_{r}\times \max(N_{x},1)\times \max(N_{y},1)\times \max(N_{z},1)$ +\item for $F_{t}=$4, $N_{k}=N_{r}$; +\item for $F_{t}=$8 or 9, $N_{k}=N_{x}\times \max(N_{z},1)$; +\item for $F_{t}=$12 or 13, $N_{k} = 6\times N_{x}^{2}\times \max(N_{z},1)$; +\item for $F_{t}=$20, 21, 22 or 23, $N_{k} = (N_{r}+1)\times \max(N_{x},1)\times \max(N_{y},1)\times \max(N_{z},1)$; +\item for $F_{t}=$24 or 25, $N_{k} = (N_{r}+1)\times \max(N_{z},1)$. +\end{itemize} + +\item The maximum number of mixtures used in this geometry $M_{m}=\mathcal{S}^{G}_{7}$ + +\item The cell flag $F_{c}=\mathcal{S}^{G}_{8}$ +\begin{displaymath} +F_{c} = \left\{ +\begin{array}{rl} + 0 & \textrm{Cell option not activated} \\ + 1 & \textrm{Cell option present} +\end{array} \right. +\end{displaymath} + +\item The number of sub-geometries defined in this geometry $F_{g}=\mathcal{S}^{G}_{9}$ + +\item The merge flag $F_{m}=\mathcal{S}^{G}_{10}$ +\begin{displaymath} +F_{m} = \left\{ +\begin{array}{rl} + 0 & \textrm{Merge option not activated} \\ + 1 & \textrm{Merge option present} +\end{array} \right. +\end{displaymath} + +\item The split flag $F_{s}=\mathcal{S}^{G}_{11}$ +\begin{displaymath} +F_{s} = \left\{ +\begin{array}{rl} + 0 & \textrm{Split option not activated} \\ + 1 & \textrm{Split option present} \\ + 2 & \textrm{Split option present. The embedded tubes are not splitted.} +\end{array} \right. +\end{displaymath} + +\item The double heterogeneity flag $F_{\mathrm{dh}}=\mathcal{S}^{G}_{12}$ +\begin{displaymath} +F_{\mathrm{dh}} = \left\{ +\begin{array}{rl} + 0 & \textrm{Double heterogeneity option not activated} \\ + 1 & \textrm{Double heterogeneity option present} +\end{array} \right. +\end{displaymath} + +\item The number of cluster sub-geometry $N_{\mathrm{cl}}=\mathcal{S}^{G}_{13}$ + +\item The type of sectorizarion $F_{\mathrm{sec}}=\mathcal{S}^{G}_{14}$. +This information may be given only if $F_{t}\ge 20$. +\begin{displaymath} +F_{\mathrm{sec}} = \left\{ +\begin{array}{rl} +-999 & \textrm{non-sectorized cell processed as a sectorized cell} \\ +-1 & \textrm{$\times$--type sectorization} \\ + 0 & \textrm{non-sectorized cell} \\ + 1 & \textrm{$+$--type sectorization} \\ + 2 & \textrm{simultaneous $\times$-- and $+$--type sectorization} \\ + 3 & \textrm{simultaneous $\times$-- and $+$--type sectorization shifted by 22.5$^\circ$} \\ + 4 & \textrm{windmill-type sectorization.} +\end{array} \right. +\end{displaymath} + +\item Number of tubes that are {\sl not} splitted by the sectors if $F_{\mathrm{sec}}\ne 0$. This integer is selected in interval $0 \le F_{\mathrm{sec2}} \le N_{r}$. $F_{\mathrm{sec2}}=\mathcal{S}^{G}_{15}$. + +\item The pin location option $\mathcal{S}^{G}_{18}$. When $\mathcal{S}^{G}_{18}>0$, the pin are located according to $(r,\theta)$ in 2-D and 3-D (center along the cylinder axis in the cell into which they are inserted) while for $\mathcal{S}^{G}_{18}<0$, the pin are +located according to $(x,y)$ in 2-D and $(x,y,z)$ in 3-D. A value of $\mathcal{S}^{G}_{18}=0$, implies that there is no pin in the geometry. + +\end{itemize} + +\vskip 0.2cm + +The radii of a {\tt CARCEL}-- or {\tt HEXCEL}--type geometry are defined as +shown in the following figure: + +\vbox{ +\begin{center} +\epsfxsize=5.5cm +\centerline{ \epsffile{radius.eps}} +\end{center} } + +In case where $F_{\mathrm{sec}}\ne 0$, the elementary cell is splitted with +sectors. Mixture indices are specific in each splitted region. They are defined +as in the following two figures ({\tt isect}$\equiv F_{\mathrm{sec}}$ and {\tt jsect}$\equiv F_{\mathrm{sec2}}$): + +\vbox{ +\begin{center} +\epsfxsize=16cm +\centerline{ \epsffile{rect3c.eps}} +\end{center} } + +\vbox{ +\begin{center} +\epsfxsize=13cm +\centerline{ \epsffile{hexa3c.eps}} +\end{center} } + +\vskip 0.2cm + +In case of an automatic geometry definition using the \moc{NAP:} module, the number of mixtures corresponding to assembly in the original core definition is named $N_{mxa}$ and the number of assembly along X and Y directions are $N_{ax}$ and $N_{ay}$ respectively. + +\subsection{The main \dir{geometry} directory}\label{sect:geometrydirmain} + +On its first level, the +following records and sub-directories will be found in the \dir{geometry} directory: + +\begin{DescriptionEnregistrement}{Main records and sub-directories in \dir{geometry}}{7.5cm} +\CharEnr + {SIGNATURE\blank{3}}{$*12$} + {Signature of the data structure ($\mathsf{SIGNA}=${\tt L\_GEOM\blank{6}})} +\IntEnr + {STATE-VECTOR}{$40$} + {Vector describing the various parameters associated with this data structure $\mathcal{S}^{G}_{i}$, + as defined in \Sect{geometrystate}.} +\IntEnr + {MIX\blank{9}}{$N_{k}$} + {Record containing the material mixture index $1\le i \le M_m$ per region (for positive indices) or + the sub-geometry index $1\le |i| \le F_g$ per region (for negative indices). {\tt MIX(I)} is set to + zero in voided regions {\tt I} or in regions located outside the domain.} +\OptIntEnr + {HMIX\blank{8}}{$N_{k}$}{*} + {array $H_{i}$ containing the virtual (homogenization) mixtures associated with different regions of the geometry} +\OptRealEnr + {RADIUS\blank{6}}{$N_{r}+1$}{$N_{r}\ge 1$}{cm} + {The radial mesh $R_{i}$ position. The first element of this vector is identical to 0.0} +\OptRealEnr + {OFFCENTER\blank{3}}{$3$}{$N_{r}\ge 1$}{cm} + {The displacement of the center of the annular mesh from the center of a Cartesian cell} +\OptRealEnr + {MESHX\blank{7}}{$N_{x}+1$}{$N_{x}\ge 1$}{cm} + {The $x-$directed mesh position $X_{i}$} +\OptRealEnr + {MESHY\blank{7}}{$N_{y}+1$}{$N_{y}\ge 1$}{cm} + {The $y-$directed mesh position $Y_{i}$} +\OptRealEnr + {MESHZ\blank{7}}{$N_{z}+1$}{$N_{z}\ge 1$}{cm} + {The $z-$directed mesh position $Z_{i}$} +\OptRealEnr + {SIDE\blank{8}}{$1$}{${{\displaystyle 8\le F_{t}\le 11} \atop \displaystyle {24\le F_{t}\le 25}}$}{cm} + {The width of the side of the hexagon $H$} +\OptIntEnr + {SPLITR\blank{6}}{$N_{r}+1$}{$F_{s}\times N_{r}\ge 1$} + {Record containing the radial mesh splitting $S_{r,i}$. A negative value permits a splitting into + equal sub-volumes; a positive value permits a splitting into equal sub-radius spacings} +\OptIntEnr + {SPLITX\blank{6}}{$N_{x}$}{$F_{s}\times N_{x}\ge 1$} + {Record containing the $x-$directed mesh splitting $S_{x,i}$} +\OptIntEnr + {SPLITY\blank{6}}{$N_{y}$}{$F_{s}\times N_{y}\ge 1$} + {Record containing the $y-$directed mesh splitting $S_{y,i}$} +\OptIntEnr + {SPLITZ\blank{6}}{$N_{z}$}{$F_{s}\times N_{z}\ge 1$} + {Record containing the $z-$directed mesh splitting $S_{z,i}$} +\OptIntEnr + {SPLITH\blank{6}}{$1$}{$F_{t}=12,13$} + {value $S_{h}$ of the triangular mesh splitting for triangular hexagons in the geometry. This will lead to a spatial triangular mesh spacing of $H_{s}=H/N_{x}$} +\OptIntEnr + {SPLITL\blank{6}}{$1$}{$F_{t}=8,9$} + {value $S_{h}$ of the lozenge mesh splitting for hexagons in the geometry. This will lead to $3 \times${\tt SPLITL}$^2$ lozenges per hexagon. If unset, the default value is {\tt SPLITL} $=1$.} +\OptIntEnr + {IHEX\blank{8}}{$1$}{$F_{t}= 8,9,12,13,24,25$} + {The type of hexagonal symmetry $\beta_{h}$} +\IntEnr + {NCODE\blank{7}}{$6$} + {Record containing the types of boundary conditions on each surface + $N_{\beta,j}$. {\tt NCODE(1)}: {\tt X-} or {\tt HBC} condition; + {\tt NCODE(2)}: {\tt X+} or {\tt R+} condition; {\tt NCODE(3)}: {\tt Y-} + condition; {\tt NCODE(4)}: {\tt Y+} condition; {\tt NCODE(5)}: {\tt Z-} + condition; {\tt NCODE(6)}: {\tt Z+} condition} +\RealEnr + {ZCODE\blank{7}}{$6$}{} + {Record containing the albedo value on each surface $\beta_{j}$} +\IntEnr + {ICODE\blank{7}}{$6$} + {Record containing the albedo index on each surface $I_{\beta,j}$. + The vector $\beta_{j}$ is used only if $I_{\beta,j}>0$ and $N_{\beta,j}=6$. In the case where + $I_{\beta,j}<0$ and $N_{\beta,j}=6$ the + vector $\beta_{p,j}$ in the directory \dir{macrolib} is used} +\OptIntEnr + {NPIN\blank{8}}{$1$}{$|\mathcal{S}^{G}_{18}|\ne 0$} + {Number $N_{\text{pin}}$ of identical pins in a cluster. All the pins will see identical flux} +\OptRealEnr + {DPIN\blank{8}}{$1$}{$|\mathcal{S}^{G}_{18}|\ne 0$}{cm$^{-3}$} + {Relative density $d_{p,r}$ of pins in a cluster. In this case $N_{\text{pin}}=-1$} +\OptRealEnr + {RPIN\blank{8}}{$k$}{$\mathcal{S}^{G}_{18}=1$}{cm} + {array $R_{\text{pin},j}$ containing the radial positions at which the center of the pins in the cluster are located with respect to the center of the cell ($k=N_{\text{pin}}$). In the case where + $R_{\text{pin},j}$ contains a single element ($k=1$), it is assumed that the pins are all located at the same radial position $R_{\text{ref}}=R_{\text{pin},1}$} +\OptRealEnr + {APIN\blank{8}}{$k$}{$\mathcal{S}^{G}_{18}=1$}{rad} + {array $\theta_{\text{pin},j}$ containing the angular positions at which the center of the pins in the cluster are located with respect to the $x$, $y$ or $z$ axis +respectively for \moc{TUBEX}, \moc{TUBEY} and \moc{TUBEZ} geometry ($k=N_{\text{pin}}$). In the case where + $\theta_{\text{pin},j}$ contains a single element ($k=1$), it is assumed that the first pin is located at $\theta_{\text{ref}}=\theta_{\text{pin},1}$, the remaining pins being located at +$\theta_{\text{pin},j}=\theta_{\text{ref}}+2(j-1)\pi/N_{\text{pin}}$} +\OptRealEnr + {CPINX\blank{7}}{$N_{\text{pin}}$}{$\mathcal{S}^{G}_{18}=-1$}{cm} + {array $X_{\text{pin},j}$ containing the $x$ positions at which the pins in the cluster are centered with respect to the center of the cell} +\OptRealEnr + {CPINY\blank{7}}{$N_{\text{pin}}$}{$\mathcal{S}^{G}_{18}=-1$}{cm} + {array $Y_{\text{pin},j}$ containing the $y$ positions at which the pins in the cluster are centered with respect to the center of the cell} +\OptRealEnr + {CPINZ\blank{7}}{$N_{\text{pin}}$}{$\mathcal{S}^{G}_{18}=-1$}{cm} + {array $Z_{\text{pin},j}$ containing the $z$ positions at which the pins in the cluster are centered with respect to the center of the cell} +\OptDirEnr + {BIHET\blank{7}}{$F_{dh}=1$} + {Directory containing double-heterogeneity related data. This directory can only be present on the root directory.} +\OptRealEnr + {POURCE\blank{6}}{$\mathcal{S}^{G}_{3}$}{$F_{t}=30$}{} + {The proportion of each cell type in the lattice $P_{j}$} +\OptRealEnr + {PROCEL\blank{6}}{$\mathcal{S}^{G}_{3},\mathcal{S}^{G}_{3}$}{$F_{t}=30$}{} + {The pre-calculated probability for a neutron leaving a cell of type $i$ to enter in a + cell of type $j$ without crossing any other cell $P_{i,j}$} +\OptCharEnr + {CELL\blank{8}}{$(F_{g})*12$}{$F_{c}=1$} + {The names of the sub-geometries ($\mathsf{CELL}_{k}$)} +\OptIntEnr + {MERGE\blank{7}}{$N_{k}$}{$F_{m}=1$} + {The merging index corresponding to each region $G_{m,i}$} +\OptIntEnr + {TURN\blank{8}}{$N_{k}$}{$F_{c}=1$} + {The orientation index corresponding to each region $G_{t,i}$. Negative values are used to turn a cell in the Z direction.} +\OptCharEnr + {CLUSTER\blank{5}}{$(F_{cl})*12$}{$F_{cl}\ge 1$} + {The names of the sub-geometries making up the cluster ($\mathsf{CLUSTER}_{k}$)} +\OptDirVar + {\listedir{subgeo}}{$F_{g}\ge 1$} + {Set of sub-directories containing a subgeometry} +\OptCharEnr + {MIX-NAMES\blank{3}}{$(M_{m})*12$}{*} + {The names of the mixtures} +\IntEnr + {A-NX\blank{8}}{$N_{ay}$}{Number of assemblies on each row} +\IntEnr + {A-IBX\blank{7}}{$N_{ay}$}{Position of the first assembly on each row} +\IntEnr + {A-ZONE\blank{6}}{$N_{ch}$}{Number of the assembly associated with each channel. Each assembly may be represented by several channels if they have been heterogeneously homogenized.} +\IntEnr + {A-NMIXP\blank{5}}{1}{The number of mixtures in one heterogeneously homogenized assembly. $N_{mxp}$. Note for homogeneously homogenized assembly $N_{mxp}$ = 1.} +\end{DescriptionEnregistrement} + +In the case where a cylindrical correction is applied over a full--core Cartesian +calculation, the following additional data is provided. It is provided if and only if type 20 +({\tt CYLI}) boundary conditions are set in the $X$--$Y$ plane (see \Fig{corr}). + +\begin{figure}[h!] +\begin{center} +\epsfxsize=5cm +\centerline{ \epsffile{Fig6.eps}} +\parbox{14cm}{\caption{Cylindrical correction in Cartesian geometry} +\label{fig:corr}} +\end{center} +\end{figure} + +\begin{DescriptionEnregistrement}{Cylindrical correction related records in \dir{geometry}}{7.5cm} +\RealEnr + {XR0\blank{9}}{$N_{\rm cyl}$}{cm} + {Record containing the coordinate of the $Z$ axis from which the cylindrical correction is applied to + Cartesian geometries. $N_{\rm cyl}$ is the number of radii.} +\RealEnr + {RR0\blank{9}}{$N_{\rm cyl}$}{cm} + {Record containing the radius of the real cylindrical boundary (rrad).} +\RealEnr + {ANG\blank{9}}{$N_{\rm cyl}$}{1} + {Record containing the angle (in radian) of the cylindrical notch. \dusa{ang}(ir) $= {\pi \over 2}$ by default (i.e. the correction is applied at every angle).} +\end{DescriptionEnregistrement} + +The type of hexagonal symmetry $\beta_{h}$ is defined as: +\begin{displaymath} +\beta_{h} = \left\{ +\begin{array}{rl} + 1 & \textrm{S30} \\ + 2 & \textrm{SA60} \\ + 3 & \textrm{SB60} \\ + 4 & \textrm{S90} \\ + 5 & \textrm{R120} \\ + 6 & \textrm{R180} \\ + 7 & \textrm{SA180} \\ + 8 & \textrm{SB180} \\ + 9 & \textrm{COMPLETE} +\end{array} \right. +\end{displaymath} + +\textrm{S30}, \textrm{SA60} and \textrm{COMPLETE} symmetries are depicted in the following figures. The other types of hexagonal symmetries are defined in the DRAGON users guide.\cite{Dragon5} + +\vbox{ +\begin{center} +\epsfxsize=9cm +\centerline{ \epsffile{hexs30.eps}} +\end{center} } +\vbox{ +\begin{center} +\epsfxsize=6cm +\centerline{ \epsffile{hexcomp.eps}} +\end{center} } + +{\tt NCODE} is a record containing the types of boundary conditions on each surface. In Cartesian geometry, the 6 components of {\tt NCODE} are related to sides {\tt X-}, {\tt X+}, {\tt Y-}, {\tt Y+}, {\tt Z-} and {\tt Z+}, respectively. The possibilities are: +\begin{displaymath} +N_{\beta,j} = \left\{ +\begin{array}{rl} + 0 & \textrm{side not used} \\ + 1 & \textrm{{\tt VOID}: zero +re-entrant angular flux. This side is an external surface of the domain.} \\ + 2 & \textrm{{\tt REFL}: reflection boundary condition. In +most DRAGON calculations, this implies} \\ + & \textrm{white boundary conditions. In DRAGON the cell is never unfolded to take into} \\ +& \textrm{account a REFL boundary condition.} \\ + 3 & \textrm{{\tt DIAG}: diagonal boundary condition. The side under consideration +has the same} \\ +& \textrm{properties as that associated with a diagonal through the +geometry. Note that two} \\ + & \textrm{and only two {\tt DIAG} sides must be specified. The +diagonal symmetry is only permitted} \\ + & \textrm{for square geometry and in the following +combinations: ({\tt X+} and {\tt Y-}) or ({\tt X-} and {\tt Y+})} \\ + 4 & \textrm{{\tt TRAN}: translation boundary condition. The side under consideration +is connected} \\ +& \textrm{to the opposite side of a Cartesian domain. This option +provides the facility to treat} \\ + & \textrm{an infinite geometry with translation +symmetry. The only combinations of} \\ + & \textrm{translational symmetry permitted are related to sides ({\tt X-} and {\tt X+}) and/or} \\ + & \textrm{({\tt Y-} and {\tt Y+}) and/or ({\tt Z-} and {\tt Z+}).} \\ + 5 & \textrm{{\tt SYME}: symmetric reflection boundary condition. The side under consideration +is} \\ +& \textrm{located outside the domain and that a reflection symmetry is associated with the} \\ +& \textrm{adequately directed axis running through the center of the cells closest to this side.} \\ + 6 & \textrm{{\tt ALBE}: albedo boundary condition. The side under consideration has an +arbitrary} \\ +& \textrm{albedo with a real value given in the record {\tt `ZCODE'} or indexed by the record} \\ + & \textrm{{\tt `ICODE'}. This side is an external surface of the domain.} \\ + 7 & \textrm{{\tt ZERO}: zero flux boundary condition. This side is an external surface of the domain.} \\ + 8 & \textrm{{\tt PI/2}: $\pi$/2 rotation. The side under consideration is characterized by a $\pi / 2$ symmetry.} \\ + & \textrm{The only $\pi / 2$ symmetry permitted is related to sides ({\tt X-} and {\tt Y-}). This condition can} \\ + & \textrm{be combined with a translation boundary condition:({\tt PI/2 X- TRAN X+}) and/or} \\ + & \textrm{({\tt PI/2 Y- TRAN Y+}).} \\ + 9 & \textrm{{\tt PI}: $\pi$ rotation} \\ +10 & \textrm{{\tt SSYM}: specular relexion boundary condition. Such a condition may be +obtained by} \\ + & \textrm{unfolding the geometry.} \\ +20 & \textrm{{\tt CYLI}: use a cylindrical correction in full--core Cartesian geometry} +\end{array} \right. +\end{displaymath} + +In cylindrical geometry, the 3 components of {\tt NCODE} are related to sides {\tt R+}, {\tt Z-} and {\tt Z+}, respectively. The possibilities are: {\tt VOID}, {\tt REFL}, {\tt ALBE} and/or {\tt ZERO}. + +\vskip 0.2cm + +In hexagonal geometry, the 3 components of {\tt NCODE} are related to sides {\tt H+} (the surface surrounding the hexagonal domain in the X--Y plane), {\tt Z-} and {\tt Z+}, respectively. The possibilities are: {\tt VOID}, {\tt REFL}, {\tt SYME}, {\tt ALBE} and/or {\tt ZERO}. + +\vskip 0.2cm + +We will now describe the exact meaning of the orientation index $G_{t,i}$. For Cartesian geometries, the eight +possible orientations are shown in the following figure: + +\begin{center} +\epsfxsize=8cm +\centerline{ \epsffile{oricart.eps}} +\end{center} + +For hexagonal geometries, the twelve +possible orientations are shown in the following figure: + +\begin{center} +\epsfxsize=10cm +\centerline{ \epsffile{orihex.eps}} +\end{center} + +In the case where $F_{c}=1$, the set of directory \listedir{subgeo} will have the +same name as the variable $\mathsf{CELL}_{k}$. For example, in the case where +$F_{g}=2$ and +\begin{displaymath} +\mathsf{CELL}_{k} = \left\{ +\begin{array}{lll} +\mathtt{GEO1} & \textrm{for} & k=1\\ +\mathtt{GEO2} & \textrm{for} & k=2 +\end{array} \right. +\end{displaymath} +then +the following directories will also be present in the main geometry directory: + +\begin{DescriptionEnregistrement}{Cell sub-geometry directory}{7.0cm} +\DirEnr + {GEO1\blank{8}} + {A first \dir{geometry} directory} +\DirEnr + {GEO2\blank{8}} + {A second \dir{geometry} directory} +\end{DescriptionEnregistrement} + +In the case where $F_{cl}\ge1$, the set of directory \listedir{subgeo} will have the +same name as the variable $\mathsf{CLUSTER}_{k}$. For example, in the case where +$F_{cl}=2$ and +\begin{displaymath} +\mathsf{CLUSTER}_{k} = \left\{ +\begin{array}{lll} +\mathtt{RODS1} & \textrm{for} & k=1\\ +\mathtt{RODS2} & \textrm{for} & k=2 +\end{array} \right. +\end{displaymath} +then +the following directories will also be present in the main geometry directory: + +\begin{DescriptionEnregistrement}{Cluster sub-geometry directory}{7.0cm} +\OptDirEnr + {RODS1\blank{7}}{$F_{g}\ge 1$} + {A first \dir{geometry} directory} +\OptDirEnr + {RODS2\blank{7}}{$F_{g}\ge 1$} + {A second \dir{geometry} directory} +\end{DescriptionEnregistrement} + +\subsection{The \moc{/BIHET/} sub-directory in \dir{geometry}}\label{sect:geometrybihet} + +The first level of the geometry directory may contains a double-heterogeneity directory \moc{/BIHET/} made of the +following records: + +\begin{DescriptionEnregistrement}{Records in the \moc{/BIHET/} sub-directory}{7.5cm} +\IntEnr + {STATE-VECTOR}{$40$} + {Vector describing the various parameters associated with this data structure $\mathcal{S}^{dh}_{i}$} +\IntEnr + {NS\blank{10}}{$\mathcal{S}^{dh}_{1}$} + {The number of sub-regions in the micro-structures $N_{\mathrm{micro},i}$} +\RealEnr + {RS\blank{10}}{$\mathcal{S}^{dh}_{2},\mathcal{S}^{dh}_{1}$}{cm} + {The radii of the tubes or spherical shells making up the micro-structures + $R_{\mathrm{micro},i,j}$} +\IntEnr + {MILIE\blank{7}}{$\mathcal{S}^{dh}_{3}$} + {The composite mixture indices used in the definition of the macro-geometry $C_{\mathrm{micro},i,j}$} +\IntEnr + {MIXDIL\blank{6}}{$\mathcal{S}^{dh}_{3}$} + {The mixture indices associated with the diluent in each composite mixtures of the macro-geometry $D_{\mathrm{micro},i,j}$} +\IntEnr + {MIXGR\blank{7}}{$\mathcal{S}^{dh}_{4},\mathcal{S}^{dh}_{3}$} + {The mixture indices associated with each region of the micro-structures $M_{\mathrm{micro},i,j}$} +\RealEnr + {FRACT\blank{7}}{$\mathcal{S}^{dh}_{1},\mathcal{S}^{dh}_{3}$}{} + {The volumetric concentration of each micro-structure $\rho_{\mathrm{micro},i,j}$} +\end{DescriptionEnregistrement} + +The dimensioning parameters for this data structure, which are stored in the state vector +$\mathcal{S}^{bh}$, represent: + +\begin{itemize} + +\item The number of different kinds of macro-structures $\mathcal{S}^{dh}_{1}$ + +\item $1$ plus the maximum number of annular sub-regions in any micro-structure +$\mathcal{S}^{dh}_{2}$ + +\item The number of composite mixtures to be included the macro-geometry $\mathcal{S}^{dh}_{3}$ + +\item The maximum number of annular sub-regions in the micro-structure +$\mathcal{S}^{dh}_{4}=(\mathcal{S}^{dh}_{2}-1)\times \mathcal{S}^{dh}_{1}$ + +\item The type of micro-structure $\mathcal{S}^{dh}_{5}$ +\noindent where +\begin{displaymath} +\mathcal{S}^{dh}_{5} = \left\{ +\begin{array}{rl} + 3 & \textrm{Tubular micro-structure} \\ + 4 & \textrm{Spherical micro-structure} \\ +\end{array} \right. +\end{displaymath} +\end{itemize} + +\clearpage |