A Time-Dependent, Three-Dimensional Neutron Transport Methodology
Sedat Goluoglu H.L. Dodds
University of Tennessee
Codes:
TORT: Three-dimensional, discrete ordinates code
TDTORT: time-dependent version of TORT
Assumptions:
- Energy spectrum of prompt neutrons and precurser groups are space independent
Notes:
- Quasi-static method is a flux synthesis method to solve the time-dependent Boltzmann transport eq
- Time-dependent flux is product of slowly varying shape function (space/energy/angle) and rapidly varying amplitude function
- Factorization is unique because of a normalization condition
- Shape eq. is only solved when needed, amplitude function (simpler) is solved frequently over small time intervals
- Normalization condition looks like the one from Henry (1958)
- The shape equation is solved, the result is used to calculate parameters via inner prodcuts, then time-dependent ampl. and precurser eqs are solved with those inner products.
- Transport Eq is solved with
TORT, time derivative is approximated by a backward difference approach - Shape function is calculated by using the normalization condition
from earlier, then the amplitude function is calculated by solving
the kinetics eqs with the
LSODEsolver. - Transient 1: single step perturbation at time 0, cross sections are changed to simulate a step change in materials
- Transient 2: step at time 0, second step added at a later time
- Transient 3: step at time 0, followed by ramp starting at time 0
- Transient 4: ramp starting at time 0