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One-speed neutron diffusion in a finite medium

Steady State Diffusion Equation. One-speed neutron diffusion in a finite medium. At the interface What if A or B is a vacuum? Linear extrapolation distance. A B. x. More realistic multiplying medium. One-speed neutron diffusion in a multiplying medium.

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One-speed neutron diffusion in a finite medium

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  1. Steady State Diffusion Equation One-speed neutron diffusion in a finite medium • At the interface • What if A or B is a vacuum? • Linear extrapolation distance. A B x Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  2. More realistic multiplying medium One-speed neutron diffusion in a multiplying medium • The reactor core is a finite multiplying medium. • Neutron flux? • Reaction rates? • Power distribution in the reactor core? • Recall: • Critical (or steady-state): • Number of neutrons produced by fission = number of neutrons lost by: • absorption • and • leakage Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  3. More realistic multiplying medium Things to be used later…! Recall: For a critical reactor: Keff = 1 K > 1 Steady state homogeneous reactor multiplying medium Material buckling Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  4. More on One-Speed Diffusion HW 20 Show that for a critical homogeneous reactor Infinite Bare Slab Reactor (one-speed diffusion) z  • Vacuum beyond. • Return current = 0. • d = linear extrapolation distance • = 0.71 tr (for plane surfaces) • = 2.13 D. Reactor x a/2 a a0/2 d d Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  5. More on One-Speed Diffusion HW 21 For the infinite slab . Show that the general solution with BC’s Flux is symmetric about the origin.  Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  6. More on One-Speed Diffusion HW 21 (continued) Fundamental mode, the only mode significant in critical reactors. For a critical reactor, the geometrical buckling is equal to the material buckling. To achieve criticality Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  7. More on One-Speed Diffusion • To achieve criticality • But criticality at what power level?? • 0 can not be determined by the geometry alone. Do it. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  8. More realistic multiplying medium • The buckling is a measure of extent to which the flux curves or “buckles.” • For a slab reactor, the buckling goes to zero as “a” goes to infinity. There would be no buckling or curvature in a reactor of infinite width. • Buckling can be used to infer leakage. The greater the curvature, the more leakage would be expected. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  9. More on One-Speed Diffusion Spherical Bare Reactor (one-speed diffusion) Cube Sphere Minimum leakage  minimum fuel to achieve criticality.  HW 22 r  Reactor Continue! r0 Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  10. More on One-Speed Diffusion HW 23 Infinite planer source in an infinite medium.   HW 24 ? Infinite planer source in a finite medium. x a/2 a a0/2 Source Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  11. More on One-Speed Diffusion Infinite planer source in a multi-region medium. Infinite Finite Infinite  Project 2 Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

  12. Back to Multiplication Factor Things to be used later…! k = fp,  • Fast from thermal, • Fast from fast, . • Thermal from fast, p. • Thermal available for fission • Thinking QUIZ • For each thermal neutron absorbed, how many fast neutrons are produced? Recall: Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh).

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