Data in Nuclear Engineering

Kathryn (Katy) Huff

Nuclear Engineering and Engineering Physics, University of Wisconsin - Madison

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

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

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

\[\gamma(f, i)\]

\[i\]

\[E\]

nuclear structure

Evaluated Nuclear Data Sets

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

Experiments

Experiments

Nuclear Data is for Simulations

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

MSBR Full Core Simulation

(Robertson, 1979)

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

MSBR Full Core Simulation

Andrei Rykhlevskii

Reactor Kinetics

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

\[k=1\]

Reactivity

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

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

Point Reactor Kinetics

\[ \begin{align} p &= \mbox{ reactor power }\\ \rho(t,&T_{fuel},T_{cool},T_{mod}, T_{refl}) = \mbox{ reactivity}\\ \beta &= \mbox{ fraction of neutrons that are delayed}\\ \beta_j &= \mbox{ fraction of delayed neutrons from precursor group j}\\ \zeta_j &= \mbox{ concentration of precursors of group j}\\ \lambda_{d,j} &= \mbox{ decay constant of precursor group j}\\ \Lambda &= \mbox{ mean generation time }\\ \omega_k &= \mbox{ decay heat from FP group k}\\ \kappa_k &= \mbox{ heat per fission for decay FP group k}\\ \lambda_{FP,k} &= \mbox{ decay constant for decay FP group k}\\ T_i &= \mbox{ temperature of component i} \end{align} \]

\[ \frac{d}{dt}\left[ \begin{array}{c} p\\ \zeta_1\\ .\\ \zeta_j\\ .\\ \zeta_J\\ \omega_1\\ .\\ \omega_k\\ .\\ \omega_K\\ T_{i}\\ .\\ T_{I}\\ \end{array} \right] = \left[ \begin{array}{ c } \frac{\rho(t,T_{i},\cdots)-\beta}{\Lambda}p + \displaystyle\sum^{j=J}_{j=1}\lambda_{d,j}\zeta_j\\ \frac{\beta_1}{\Lambda} p - \lambda_{d,1}\zeta_1\\ .\\ \frac{\beta_j}{\Lambda}p-\lambda_{d,j}\zeta_j\\ .\\ \frac{\beta_J}{\Lambda}p-\lambda_{d,J}\zeta_J\\ \kappa_1p - \lambda_{FP,1}\omega_1\\ .\\ \kappa_kp - \lambda_{FP,k}\omega_k\\ .\\ \kappa_{k p} - \lambda_{FP,k}\omega_{k}\\ f_{i}(p, C_{p,i}, T_{i}, \cdots)\\ .\\ f_{I}(p, C_{p,I}, T_{I}, \cdots)\\ \end{array} \right] \]

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.)