NE 452552 Nuclear Reactor Analysis II

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NE 452/552Nuclear Reactor Analysis II

• Lecture 8Group collapse
• Intro to MULTIFLUX

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What is a group collapse?

• Often times, we may need to take data from a
  dataset calculated with a fine group structure
  (many energy groups) and use it in a multigroup
  model with fewer groups, or a coarse group
  structure.
• To do this, the data must be group collapsed.

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What is the principle behind the group collapse?

• The basic idea comes from the definition of the
  multigroup cross-section set. Suppose we have
  the following energy range with four fine
  groups and two coarse groups

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2
I
Coarse groups
Fine groups
3
II
4
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How do we perform the collapse?

• The reaction rates in the single coarse fast
  group must equal the sum of the reaction rates in
  the three fine fast groupsNow, the flux in
  the single coarse fast group is the integral of
  the flux (or, more correctly, the spectrum) over
  the energy range

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So, this gives us equations for most of the
coarse group cross-sections

• Absorption can be found by
• We can also do the diffusion coefficient and
  nu-sigma-f terms this way.
• What about the removal term? Well, removal has
  two pieces

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The removal cross-section...

• We already know how to do the absorption term.
  What about the downscatter term?
• We again need to set the reaction rates in coarse
  and fine group structures equal to each
  otherGraphically, this means

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The slowing cross-section

• So, the slowing cross-section is collapsed
  using
• Then our removal cross-section is found by

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So, this tells us how to perform the group
collapse, if we have the fluxes...

• So how do we calculate the fluxes?
• We first write the multigroup diffusion equations
  for the fine energy group structure

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Calculating the fluxes...

• Now, we can proceed in two ways
• Assume an infinite medium
• Assume a finite medium and associated buckling
• Going with the infinite medium approach, our
  equations become

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Calculating the fluxes...

• Now, since we are solving an eigenvalue problem,
  we have the freedom to choose a normalization for
  the fluxes. We choose the most convenient
  normalization we can
• Our flux equations then become very simple

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O.k. Lets talk about the MULTIFLUX code.

• What is MULTIFLUX?
• 2-d (xy geometry), multigroup diffusion code, for
  solving reactor flux and power profile problems
• Up to nine material types
• Either vacuum or reflecting boundary conditions
• Iterates using Inverse Power Iteration
• Uses a finite-difference technique to solve for
  fluxes at the center of each node (cell, zone)
• Written by a graduate student of Alan Robinsons
• Nodes are assumed to be square

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MULTIFLUX, cont

• Where is MULTIFLUX?
• /usr/local/neapps/bin/multiflux_c_sun on the Sun
  machines...
• How do I run it?
• Check to see that you are in the nuclear group by
  typing id.If nuclear does not show up, let me
  know.
• Next, copy the sample input file to your home
  directorycp /usr/local/classes/past/classes_wint
  er2002/ne/ne452/multiflux_c/multiflux_sample .
• Now, type the following commandmultiflux_c lt
  multiflux_sample gtoutputfilewhere outputfile is
  a filename of your choice