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+\subsection{The \moc{TAVG:} module}\label{sect:tavg}
+
+\vskip 0.2cm
+The \moc{TAVG:} module is used to compute the burnup integration limits for each
+fuel bundle, the axial power-shape over the fuel lattice, the channel refuelling rates
+and the reactor core-average exit burnup. All calculations using the \moc{TAVG:}
+module are performed according to the time-average model for the equilibrium-core
+conditions. The computing algorithm is based on bidirectional refuelling schemes of
+channels and average exit burnups specified over the fuel lattice, which should be
+recorded in the fuel map using the \moc{RESINI:} module.\\
+
+Note that the complete time-average calculation is a complex and iterative procedure,
+requiring of several full-core calculations (external iterations) to be performed. The main
+steps of the time-average calculation using DONJON are briefly described at the end
+of this section. The \moc{TAVG:} module can also be used to compute the instantaneous
+fuel burnups according to the channel patterned-age-model, for the fuel management
+and optimization purposes.\\
+
+\noindent
+The \moc{TAVG:} module specification is: 
+
+\begin{DataStructure}{Structure \moc{TAVG:}}
+\dusa{FMAP} \moc{:=} \moc{TAVG:} \dusa{FMAP}
+\dusa{POWER} \moc{::} \dstr{desctavg}
+\end{DataStructure}
+
+\noindent where
+
+\begin{ListeDeDescription}{mmmmmmmm}
+
+\item[\dusa{FMAP}] \texttt{character*12} name of a \dds{fmap} object,
+that will be updated by the \moc{TAVG:} module. The \dusa{FMAP} object
+must contain the average exit burnups and refuelling schemes of channels.
+
+\item[\dusa{POWER}] \texttt{character*12} name of a \dds{power} object
+containing the channel and bundle powers, previously computed by the
+\moc{FLPOW:} module. The channel and bundle powers are used by the
+\moc{TAVG:} module to compute the normalized axial power-shape over
+each channel. 
+
+\item[\dstr{desctavg}] structure describing the input data to the \moc{TAVG:} module.
+
+\end{ListeDeDescription}
+
+\vskip 0.2cm
+\subsubsection{Input data to the \moc{TAVG:} module}\label{sect:strtavg}
+
+\noindent
+Note that the input order must be respected. \\
+
+\begin{DataStructure}{Structure \dstr{desctavg}}
+$[$ \moc{EDIT} \dusa{iprint} $]$ \\
+$[$ \moc{AX-SHAPE} $[$ \moc{RELAX} \dusa{relval} $]$ $]$ \\
+$[$ \moc{B-EXIT} $]$ \\
+ ;
+\end{DataStructure}
+
+\noindent where
+\begin{ListeDeDescription}{mmmmmmmm}
+
+\item[\moc{EDIT}] keyword used to set \dusa{iprint}.
+
+\item[\dusa{iprint}] integer index used to control the printing on screen:
+ = 0 for no print; = 1 for minimum printing (default value); = 2 only the burnup limits
+over each channel are printed; = 3 only the axial power-shape values over each channel
+are printed; = 4 only the channel refuelling rates are printed; for larger values of
+\dusa{iprint} everything will be printed.
+
+\item[\moc{AX-SHAPE}] keyword used to indicate the calculation of the new
+axial power-shape and corresponding burnups limits over each reactor channel.
+
+\item[\moc{RELAX}] keyword used to set the relaxation parameter \dusa{relval}.
+
+\item[\dusa{relval}] real value of the relaxation parameter, generally used to
+control the axial-shape convergence over the external time-average iterations.
+The optimal value, which corresponds to the minimal total number of such iterations,
+can be found by performing several runs at different \dusa{relval}. The default
+value of the relaxation parameter is set to 0.5
+
+\item[\moc{B-EXIT}] keyword used to indicate the calculation of the core-average
+exit burnup and the channel refuelling rates.
+
+\end{ListeDeDescription}
+
+\vskip 0.2cm
+\subsubsection{Time-average calculation using DONJON}
+
+When the average exit burnups are provided for each channel, the exact
+burnup integration limits for each fuel bundle are unknown and need to be
+determined. The burnups integration limits are function of the normalized
+axial power-shape, which in turn depends on the flux solution over the fuel
+lattice. Moreover, the flux solution depends on the fuel-map macrolib (i.e.
+fuel properties), which in turn depends on the burnups integration limits for
+each fuel bundle. Consequently, the time-average calculation is an iterative
+procedure that consists to repeat all the steps required for the axial power-shape
+computation. This repetition is to be made until the relative error between
+the two (successives) axial power-shape calculations becomes as small
+as required for the precision.\\
+
+\noindent
+The axial power-shape computing scheme is composed of several steps,
+each step is performed using an appropriate DONJON or TRIVAC module:
+
+\begin{enumerate}
+\item An initial axial power-shape is set as a flat distribution over the fuel
+lattice and the first burnup integration limits are calculated approximately,
+using the \moc{RESINI:} module. 
+\item A time-average integration is performed and a new fuel-map \dds{macrolib}
+is created, using either \moc{NCR:}, \moc{CRE:} or \moc{AFM:} module.
+\item An extended \dds{macrolib} over the whole reactor geometry is created,
+using the \moc{MACINI:} module.
+\item If the devices are inserted into the reactor core, then the previously
+created \dds{macrolib} is to be updated for the devices properties using the
+\moc{NEWMAC:} module. 
+\item The complete \dds{macrolib} is subsequently used by the \moc{TRIVAA:}
+module in order to create a matrix \dds{system}. 
+\item The full-core numerical solution (i.e. fluxes and effective multiplication factor)
+is computed, using the \moc{FLUD:} module.
+\item The channel and bundle powers are next calculated, using the
+\moc{FLPOW:} module. 
+\item Finally, the new axial power-shape and burnup limits are computed,
+using the \moc{TAVG:} module.
+\end{enumerate}
+
+\vskip 0.1cm
+\noindent
+Note that the steps from 2 to 8 are to be repeated until the required precision
+for the axial power-shape convergence is satisfied.
+
+\clearpage