NE 455555 Nuclear Reactor Analysis II

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NE 455/555Nuclear Reactor Analysis II

• Lecture 6Inverse power iteration for
  multigroup problems
• 1, 2 and 1.5 group diffusion

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So, we know how to solve multigroup fixed source
problems. What about k?

• If we include the k-eigenvalue in our multigroup
  diffusion equations we getwhere

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We apply inverse power iteration in a way
analogous to the 1-group problem

• Begin with
• Then solve
• Compute the new k, as before

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Inverse Power Iteration, cont

• Now, we normalize the fission source
• We need to iterate this process until

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Lets look at specific examples of multigroup
systems

• First, what if you have only one group? Answer
  you get the one- group equations
• What about two-groups?

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Two group diffusion

• We choose the dividing energy E1 between the two
  energy groups so that
• (no neutrons scatter up from the
  thermal group to the fast group)
• (all fission neutrons are fast)
• Then the general two group problem is

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Two group diffusion, cont

• With our choice of dividing energy we
  obtainwhere
• We will look in more detail at these two group
  equations in our next lecture.

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One-and-a-half group diffusion?

• If we make the following approximation in our two
  group equationsthen we findand
• This equation can be solved as quickly as a
  standard one-group equation, but has some
  two-group physics built in.

Thermal neutrons are much more likely to be
absorbed than to leak out of the system.
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One-and-a-half group diffusion, cont

• This model is at the heart of the codes used to
  design most of the reactors currently in
  operation in the U.S.
• GEs FLARE code
• Siemens XTG code
• Over the last 5-8 years, most of the industry
  standard core simulator codes have gone to
  two-groups.
• Multigroup is still too expensive for the
  improvement in accuracy obtained.