NE 455555 Nuclear Reactor Analysis II

1
NE 455/555Nuclear Reactor Analysis II

• T.S. Palmer
• Winter 2000
• MWF 10-1050, RC C104

2
Course Outline

• Review of last term
• One-Group Diffusion Theory (DH Chapter 5
  207-219)
• k-eigenvalue problems (analytic and numeric)
• separation of variables

3
Course Outline, cont

• Multi-Group Diffusion Theory (DH Chapter 7
  285-307)
• heuristic derivation (Energy balance)
• derivation from energy-dependent diffusion
  equation
• types of coupling, group structure
• two-group theory, relation to six-factor formula
• one-and-a-half group theory
• group collapsing
• numerical solution of multigroup diffusion
  problems

4
Course Outline, cont

• Computer codes
• MULTIFLUX 2-d multigroup k-eigenvalue
  calculations (cores)
• CASMO 2-d integral-form multigroup transport
  calculations for cross-section generation (pin
  cells and assemblies)
• MCNP continuous energy Monte Carlo k-eigenvalue
  transport calculations (pin cells, assemblies,
  cores, ???)

5
Course Outline, cont

• Fast Spectrum Calculations (DH Chapter 8
  315-347)
• slowing down hydrogen, infinite medium, no
  absorption
• slowing down density, lethargy
• moderating power, moderating ratio
• slowing down
• hydrogen, infinite medium, absorption
• Agt1, infinite medium, no absorption
• Agt1, infinite medium, absorption
• resonance absorption hydrogen infinitely
  massive absorber
• resonance integrals NR, NRIM (or WR)
  approximations

6
Course Outline, cont

• Thermal Spectrum Calculations (DH Chapter 9
  375-395)
• thermal equilibrium
• detailed balance, the Maxwellian
• non-equilibrium spectra
• effective temperature models
• approximate models of thermalization

7
Course Outline, cont

• Heterogeneous Core Lattice Calculations (DH
  Chapter 10 398-440)
• Thermal physics
• self-shielding, disadvantage factor
• core homogenization, cell-averaging
• escape probabilities, ABH method
• Fast physics
• resonance escape, Wigner rational approximation
• rod shadowing, Dancoff factors

8
Grading

• Pencil Paper Homework 25
• Computer Homework 25
• Quizzes (5) 25
• Final Exam 25

9
Goals

• Improve your ability to interact with computers,
  both with operating systems (UNIX, in
  particular), software packages, and programming
  (yes, Virginia, there will be more
  programming...)
• Give you the capability to calculate pin-cell and
  assembly averaged cross-sections, and core power
  distributions.
• Explain (to the degree possible) the complicated
  neutron physics involved in computer codes used
  by reactor fuel designers.

10
Policies

• Late coursework
• 1-day, 75 maximum credit
• 2 or more days, NO CREDIT
• Office hours
• TTh 1-3
• Other times by appointment only
• I will not give help on homework the day before
  it is due
• Each student will get at most 20 minutes of
  instructor time per homework set.

11
Policies, cont

• Homework assignments
• Each student must turn in their own homework
  assignment unless the assignment is specifically
  labeled as a group assignment
• Programming assignments must be done
  individually. I will be checking this very
  carefully this term.

12
Review of last term

• You need to remember
• how to calculate number densities
• definitions of six-factor formula parameters
• how to solve one-group diffusion problems
• Lets work a problem(Next time)

13
Todays assignment

• Dig out your diffusion code from last term, fix
  any mistakes you may have had, and run it for the
  following problem
• A slab 100 cm thick with 100 1 cm zones. Vacuum
  boundaries on left and right. Put a source of 10
  neutrons/(cm3-sec) in the first 50 zones, zero
  source in the second 50 zones. Use a D of 2.0 cm
  and a SA of 0.1 cm-1.
• Due Friday, 1/7/00