Advanced Reactors

and Fuel Cycles

Simulation of Multiple Physics

at Disparate Scales


Kathryn (Katy) Huff

THW Software Carpentry book NCSA Logo cyclus pyrk pyne Moltres ARFC Logo

Insights at Disparate Scales

synergistic insights
science is people
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

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

Insights at Disparate Scales

synergistic insights
image generated by Anthony Scopatz, Paul P.H. Wilson, and Katy Huff

A Nuclear Fuel Cycle Simulation Framework

The Nuclear Fuel Cycle

Hundreds of discrete facilities mine, mill, convert, fabricate, transmute, recycle, and store nuclear material.

from Paul Lisowski

Fuel Cycle Metrics

  • Mass Flow
    • inventories, decay heat, radiotoxicity,
    • proliferation resistance and physical protection (PRPP) indices.
  • Cost
    • levelized cost of electricity,
    • facility life cycle costs.
  • Economics
    • power production, facility deployments,
    • dynamic pricing and feedback.
  • Disruptions
    • reliability, safety,
    • system robustness.

Current Simulators

  • CAFCA (MIT)
  • COSI (CEA)
  • DANESS (ANL)
  • DESAE (Rosatom)
  • Evolcode (CIEMAT)
  • FAMILY (IAEA)
  • GENIUSv1 (INL)
  • GENIUS v2 (UW)
  • NFCSim (LANL)
  • NFCSS (IAEA)
  • NUWASTE (NWTRB)
  • ORION (NNL)
  • MARKAL (BNL)
  • VISION (INL)

State of the Art

Performance

  • Speed interactive time scales
  • Fidelity: detail commensurate with existing challenges
  • Detail: discrete material and agent tracking
  • Regional Modeling: enabling international socio-economics

Beyond the State of the Art

Access

  • Openness: for collaboration, validation, and code sustainability.
  • Usability: for a wide range of user sophistication

Extensibility

  • Modularity: core infrastructure independent of proprietary or sensitive data and models
  • Flexibility with a focus on robustness for myriad potential developer extensions.

Extensibility

framework

Openness

private, export controlled, etc.

Growing Ecosystem


a growing number of scientists are adding modules to cyclus.

...Well Beyond

Algorithmic Sophistication

  • Efficient: memory-efficient isotope tracking
  • Customizable: constrained fuel supply
  • Dynamic: isotopic-quality-based resource routing
  • Physics-based: fuel fungibility

Agent Based Systems Analysis

An agent-based simulation is made up of actors and communications between those actors.

from Paul Lisowski

Agent Based Systems Analysis

A facility might create material.

source

Agent Based Systems Analysis

It might request material.

sink

Agent Based Systems Analysis

It might do both.

fac

Agent Based Systems Analysis

Even simple fuel cycles have many independent agents.

material flow

Dynamic Resource Exchange

abm \[N_i \subset N\]

Dynamic Resource Exchange

abm \[N_j \subset N\]

Dynamic Resource Exchange

abm \[N_i \cup N_j = N\]

Feasibility vs. Optimization

polynomial hardness

If a decision problem is in NP-C, then the corresponding optimization problem is NP-hard.

Multi-Commodity Transportation Formulation

multicommoditiy transportation problem formulation multicommoditiy transportation problem formulation

Multi-Commodity Transportation Formulation


\[ \begin{align} \min_{x} z &= \sum_{i\in I}\sum_{j\in J} c_{i,j}x_{i,j} & \\ s.t & \sum_{i\in I_s}\sum_{j\in J} a_{i,j}^k x_{i,j} \le b_s^k & \forall k\in K_s, \forall s\in S\\ & \sum_{J\in J_r}\sum_{i\in I} a_{i,j}^k x_{i,j} \le b_r^k & \forall k\in K_r, \forall r\in R\\ & x_{i,j} \in [0,x_j] & \forall i\in I, \forall j\in J \end{align} \]

Dynamic Resource Exchange

modified open

Dynamic Resource Exchange

closed

Dynamic Resource Exchange


   
     mox
-    waste
+    spent_fuel
     mox_fresh_fuel
     mox_spent_fuel

Dynamic Resource Exchange

Plutonium buildup

Transition Analysis

  • LWR to SFR
  • $T_0 = 2015$
  • $T_f <= 2215$
  • $C_0 = 100$ GWe LWR
  • Annual nuclear energy demand growth: 1%
  • Legacy LWRs have either 60-year lifetimes or 80-year lifetimes.
  • Spent LWR fuel reprocessed to fabricate FR fuel
  • Spent FR fuel reprocessed to fabricate FR fuel

Transition Analysis

power deployed by reactor type.

Power generated by reactor type.

Transition Analysis

polynomial hardness

Capacity deployed each year, by reactor type.

Detailed Metrics

possible metrics

Material Attractiveness

possible metrics

How Do We Know It's Right?

Dangerous ladies, Jezebel and Godiva

Morgan C. White talk

Quality Control

“ Organized Skepticism. Scientists are critical: All ideas must be tested and are subject to rigorous structured community scrutiny.” - R.K. Merton, 1942

Unit Checking

Pint
In PyRK, the Pint package (pint.readthedocs.org/en/0.6/) is used keeping track of units, converting between them, and throwing errors when unit conversions are not sane.

Backing Up Files

  • Good: hope
  • Better: nightly emails
  • Best: remote version control


Version Control Systems: cvs, svn, hg, git

Managing Changes

  • Good: naming convention
  • Better: clever naming convention
  • Best: local version control

Version Control.

Version Control

Docs
Keeping track of versions of the code makes it possible to experiment without fear and placing the code online encourages use and collaboration.

Automated Documentation

Docs
Automated documentation creates a browsable website explaining the most recent version of the code.

Error Detection

“ The scientific method’s central motivation is the ubiquity of error—the awareness that mistakes and self-delusion can creep in absolutely anywhere and that the scientist’s effort is primarily expended in recognizing and rooting out error. ” - Donoho, 2009.

Error Detection

  • Good: show results to experts
  • Better: integration testing
  • Best: unit test suite, continuous integration

Test Suite

Docs
The classes and functions that make up the code are tested individually for robustness using nose.

Continuous Integration

Docs
The tests are run every time a change is made to the repository online. The results are public. If a main branch has a failed test, I get an email.

Links

THE END

Katy Huff

katyhuff.github.io/2017-04-20-davis
Creative Commons License
Advanced Reactors and Fuel Cycles: Simulation of Multiple Physics at Disparate Scales by Kathryn Huff is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://katyhuff.github.io/2017-04-20-davis.

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

image generated by Tommy Cisneros and the UCBerkeley FHR group

Transient Coupled Physics

synergistic insights
image generated by Anthony Scopatz, Paul P.H. Wilson, and Katy Huff

A Nuclear Fuel Cycle Simulation Framework

Agent Based Systems Analysis


Hundreds of discrete facilities mine, mill, convert, fabricate, transmute, recycle, and store nuclear material.

from Paul Lisowski

Agent Based Systems Analysis

A facility might create material.

source

Agent Based Systems Analysis

It might request material.

sink

Agent Based Systems Analysis

It might do both.

fac

Agent Based Systems Analysis

Even simple fuel cycles have many independent agents.

material flow