Data in Nuclear Engineering


Kathryn (Katy) Huff

Physics, University of Chicago Nuclear Engineering and Engineering Physics, University of Wisconsin - Madison Nuclear Engineering, University of California, Berkeley BIDS Logo Scipy THW Software Carpentry Data Carpentry book book cyclus pyrk moltres pyne ARFC Logo NCSA Logo ANS Logo
Fission.
Chain reaction

\[\phi(E,\vec{r},\hat{\Omega},T)\]

\[\phi(E, x, y, z, \theta, \omega, T)\]

Fission.

\[\sigma(x, i, E, T)\]

Fission yield

\[\gamma(f, i)\]

Nucleus Stability

\[i\]

Resonances

\[E\]

Nucleus Stability

nuclear structure

Evaluated Nuclear Data Sets

Nuclear Resonance Theory and Evaluation

\[\sigma(x, i, E, T)=\] nuclear structure + experiments

Experiments

Schematic of a DANCE-like detector

Experiments

The DANCE detector at Los Alamos

Nuclear Data is for Simulations

PBFHR
cyclus pyrk MOOSE pyne

Simulation Methods

  • Monte Carlo Methods
  • Deterministic Methods
  • Hybrid Methods
  • Other keywords...
    • lattice codes
    • ray tracing algorithms
    • acceleration schemes
    • adjoint methods
    • ...

Application Specific Data Processing

  • Energy discretization
    • multigroup
    • pointwise
    • piecewise linear continuous
  • Angular quadratures
  • Resonance integration
  • ...

Molten Salt Reactor Designs

MSR

MSBR Full Core Simulation

MSBR

(Robertson, 1979)

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR

Reactor Kinetics

Fission.

\[\sigma(E,\vec{r},\hat{\Omega},T,x,i)\]

Chain reaction

\[k=1\]

Reactivity

\[ \begin{align} k &= \mbox{"neutron multiplication factor"}\\ &= \frac{\mbox{neutrons causing fission}}{\mbox{neutrons produced by fission}}\\ \rho &= \frac{k-1}{k}\\ \rho &= \mbox{reactivity}\\ \end{align} \]
Feedback
Delayed Neutrons

\[\beta_i, \lambda_{d,i}\]

Point Reactor Kinetics

\[ \begin{align} p &= \mbox{ reactor power }\\ \rho(t,&T_{fuel},T_{cool},T_{mod}, T_{refl}) = \mbox{ reactivity}\\ \beta &= \mbox{ fraction of neutrons that are delayed}\\ \beta_j &= \mbox{ fraction of delayed neutrons from precursor group j}\\ \zeta_j &= \mbox{ concentration of precursors of group j}\\ \lambda_{d,j} &= \mbox{ decay constant of precursor group j}\\ \Lambda &= \mbox{ mean generation time }\\ \omega_k &= \mbox{ decay heat from FP group k}\\ \kappa_k &= \mbox{ heat per fission for decay FP group k}\\ \lambda_{FP,k} &= \mbox{ decay constant for decay FP group k}\\ T_i &= \mbox{ temperature of component i} \end{align} \]
\[ \frac{d}{dt}\left[ \begin{array}{c} p\\ \zeta_1\\ .\\ \zeta_j\\ .\\ \zeta_J\\ \omega_1\\ .\\ \omega_k\\ .\\ \omega_K\\ T_{i}\\ .\\ T_{I}\\ \end{array} \right] = \left[ \begin{array}{ c } \frac{\rho(t,T_{i},\cdots)-\beta}{\Lambda}p + \displaystyle\sum^{j=J}_{j=1}\lambda_{d,j}\zeta_j\\ \frac{\beta_1}{\Lambda} p - \lambda_{d,1}\zeta_1\\ .\\ \frac{\beta_j}{\Lambda}p-\lambda_{d,j}\zeta_j\\ .\\ \frac{\beta_J}{\Lambda}p-\lambda_{d,J}\zeta_J\\ \kappa_1p - \lambda_{FP,1}\omega_1\\ .\\ \kappa_kp - \lambda_{FP,k}\omega_k\\ .\\ \kappa_{k p} - \lambda_{FP,k}\omega_{k}\\ f_{i}(p, C_{p,i}, T_{i}, \cdots)\\ .\\ f_{I}(p, C_{p,I}, T_{I}, \cdots)\\ \end{array} \right] \]
MOOSE

Coupled Multi-Physics Analysis


Using the MOOSE framework and its Jacobian-Free Newton Krylov solver, severe accident neutronics and thermal hydraulics can be simulated beautifully for simple geometries and well studied materials. (below, INL BISON work.)

from INL, Rich Williamson

Moltres: Dr. Alexander Lindsay

Moltres

Moltres Current Capabilities

  • Navier Stokes + Multi-Group Neutron Diffusion + Kinetics
  • arbitrary number of neutron energy groups
  • arbitrary number of delayed neutron precursor groups
  • neutron power coupled to salt temperature and flow
  • Precursor capability requires discontinuous galerkin upwind scheme.
  • Few group constants can be generated with SCALE-NEWT or Serpent

MSR Neutronics and TH Coupling

Moltres Base Case Moltres Base Case Moltres Base Case

MSR Precursors

Moltres Base Case Moltres Base Case

How Do We Know It's Right?

Dangerous ladies, Jezebel and Godiva

The Data Dilemma

Morgan C. White talk

Unique Issues


Export control is serious.

Export Control is a big deal in nuclear

Links

THE END

Katy Huff

katyhuff.github.io/2017-05-31-pi4
Creative Commons License
Data in Nuclear Engineering by Kathryn Huff is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://katyhuff.github.io/2017-05-31-pi4.

A Few of My Favorite Things


  • C++, Python, Fortran
  • xml, markdown, rst, $\LaTeX$
  • Doxygen, sphinx
  • CMake, conda, macports
  • GoogleTest, nose
  • hdf5, sqlite
  • cython, boost, Coin
  • jekyll, reveal.js, beamer
  • yt, matplotlib, paraview