Input for the neutronics calculation

With the fuel element geometry being fixed we can move to the generation of the nuclear cross sections. As discussed previously in section 1.4 we use the program cccmo for this purpose. We will due to time and space constraints not discuss the input required by cccmo but simply state that part of this input concerns the number densities and temperatures of the different materials in the fuel element. Since cccmo cannot accommodate variable enrichment levels within the fuel element we calculate the cross sections for the fuel element under the assumption of an average enrichment level of 2.40%. We have, furthermore, neglected the contents of burnable poison (Gd) in the fuel media. This assumption results in a highly super-critical reactor as we can see in (15.1). All the subsequent cross section generations result in homogenized cross sections in 2 energy groups which are governed by

$\begin{eqnarray*} {\mbox{Group 1: }}& & 15 {\mbox{ MeV}} \rightarrow 1.855 {\mb... ...855 {\mbox{ eV}} \rightarrow 2.2770 \cdot 10^{-3} {\mbox{ eV}} \end{eqnarray*}$

$\textstyle \parbox{1.50cm}{\begin{eqnarray} \end{eqnarray}}$

In order to calculate the number densities of the moderator it is required that we select a (saturated) state of the water and steam, (p^*,T^*). We have selected the reasonable state

$\begin{displaymath} (p^*,T^*) = (6.9{\mbox{ MPa}},284.7\mbox{${}^\circ\mbox{C}$}) \end{displaymath}$

(14.1)

$\begin{eqnarray*} \rho_f^* & \simeq & 741.78 {\mbox{ kg}}/{\mbox{m}}^3 \\ \rho_g^* & \simeq & 35.80 {\mbox{ kg}}/{\mbox{m}}^3 \end{eqnarray*}$

$\textstyle \parbox{1.50cm}{\begin{eqnarray} \end{eqnarray}}$

Furthermore, we assume the following reasonable temperatures of the cladding (Zr-2) and the moderator ( ${\mbox{H}}_2{\mbox{O}}$ )^14.2

$\begin{eqnarray*} T_{\mbox{\protect\scriptsize Zr-2}} &=& 310\mbox{${}^\circ\mb... ...mbox{\protect\scriptsize O}}} &=& 285\mbox{${}^\circ\mbox{C}$} \end{eqnarray*}$

$\textstyle \parbox{1.50cm}{\begin{eqnarray} \end{eqnarray}}$

With these assumption in place we calculate the homogenized nuclear cross sections for the fuel element for the following fuel temperatures, T_f [ ${}^\circ\mbox{C}$ ],

$\begin{displaymath} T_f = \{ 300,600,1100,1600,2100,2600 \} \mbox{${}^\circ\mbox{C}$} \end{displaymath}$

(14.2)

$\begin{displaymath} \alpha^* = \{ 0.00,0.10,0.25,0.35,0.50,0.60,0.75,0.85 \} \end{displaymath}$

(14.3)

The homogenized cross sections for the reflector regions are more difficult to calculate by means of cccmo. According to [14] the only way to obtain the cross sections is to construct a geometry of a few fuel rods surrounded by the reflector media. The fuel rods serve as a generator for a neutron flux similar in energy distribution to the flux encountered in the reactor core.

In the case with the top reflector we use 15 fuel rods^14.3 (with an amount of moderator, ie ${\mbox{H}}_2{\mbox{O}}$ , as dictated by the pitch in the fuel rod array) surrounded by 50 cm of reflector. The reflector consists of water with a steam contents which corresponds to the selected void fraction. Again we use the chosen densities given by (14.3) and select a number of void fractions given by

$\begin{displaymath} \alpha_{\mbox{\protect\scriptsize top refl}}^* = \{0.25,0.50,0.60,0.75,0.85\} \end{displaymath}$

(14.4)

The bottom reflector is modeled by 15 fuel rods surrounded by firstly 5 cm steel (corresponding to the core plate) and secondly 50 cm of reflector which in this case consists of water at the density $\rho_\ell^*$ given by (14.3). The homogenized cross sections for this geometry are shown in Appendix C.

We can now construct the input file, input_v2.neu, for the neutronics computation. The resulting input file is shown in Figure 14.2. It should be noted that due to a mistake in the neutronics input file the power level chosen for the test case is not 1800 ${\mbox{MW}}_{\mbox{\protect\scriptsize th}}$ but only 1681 ${\mbox{MW}}_{\mbox{\protect\scriptsize th}}$ --this small power level difference has, however, no noteworthy impact on the calculated results.

$\begin{figure} % latex2html id marker 43983\rule{\textwidth}{0.2mm} \begin{ve... ...re~\thefigure}\hspace{1em}Neutronics input file for the test case.}\end{figure}$