Applicability of Diffusion Theory

Applicability of Diffusion Theory

Nowadays the diffusion theory is widely used in core design of the current Pressurized Water Reactors (PWRs) or Boiling Water Reactors (BWRs). It provides a strictly valid mathematical description of the neutron flux, but it must be emphasized that the diffusion equation (in fact the Fick’s law) was derived under the following assumptions:

  1. Infinite medium
  2. No sources or sinks.
  3. Uniform medium.
  4. Isotropic scattering.
  5. Low absorbing medium.
  6. Time – independent flux.

To some extent, these limitations are valid in every practical reactor. Nevertheless the diffusion theory gives a reasonable approximation and makes accurate predictions. Nowadays reactor core analyses and design are often performed using nodal two-group diffusion methods. These methods are based on pre-computed assembly homogenized cross-sections, diffusion coefficients and assembly discontinuity factors (pin factors) obtained by single assembly calculation with reflective boundary conditions (infinite lattice). Highly absorbing control elements are represented by effective diffusion theory cross-sections which reproduce transport theory absorption rates. These pre-computed data (discontinuity factors, homogenized cross-sections, etc.) are calculated by neutron trasport codes which are based on a more accurate neutron transport theory. In short, neutron transport theory is used to make diffusion theory work.

Two methods exist for calculation of the pre-computed assembly cross-sections and pin factors.

  • Deterministic methods that solve the Boltzmann transport equation.
  • Stochastic methods that are known as Monte Carlo methods that model the problem almost exactly.

These methods are very efficient and accurate when applied to the current Pressurized Water Reactors (PWRs) or Boiling Water Reactors (BWRs).

 
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Diffusion Theory