A Time-Dependent Description of In-Core Gamma Heating in the McMaster Nuclear Reactor

Abstract

Calculating or predicting the total in-core nuclear heating is a difficult tast. Full-core models can be constructed in a Monte Carlo code, such as MCNP6 or TRIPOLI4, and will allow an analyst to calculate the prompt-gamma heating at any given in-core location; however, such codes are generally unable to track the activated or fission-product isotopes and therefore the delayed-gamma sources can't be included in such a model.

Some analysts have coupled Monte Carlo transport codes to burnup codes in an effort to include delayed-gamma sources, but the solutions tend to be reactor specific, time-independent and a lot of work. New ideas are required to calculate the total time-dependent in-core nuclear heating.

Within this report, two new models have been derived: the nuclear heating equation, and the coupled neutron and nuclear heating point kinetics (NHPK) equations. These models can be used to calculate the time and position-dependent in-core heating. The nuclear heating equations are generalized expressions of the nuclear heating in a volume of interest, within an arbitrary geometry; these equations use Monte Carlo tallies as coefficients and treat the geometry's scalar neutron flux within as the independent variable. The NHPK model describes the nuclear heating in a volume of interest, within a critical assembly by coupling nuclear heating to the famous neutron point kinetics equations.

A SCK-CEN gamma thermometer (GT) was commissioned in a materials testing reactor (MTR), the McMaster Nuclear Reactor (MNR), to measure the dynamic in-core nuclear heating in two locations. The nuclear heating equation was used to calculate self-heating of the SCK-CEN GT by neutron capture reactions. This calculation used CapGam and IAEA PGAA prompt-gamma emission data; delayed-particle emission data from NuDat 2.6 was also employed. Analysis of the GT's signal resulted in a quantitative description of the dynamic delayed-gamma heating in MNR, and provided the coefficients for the NHPK model.

The NHPK model is capable of reproducing the measured time-dependent nuclear heating, and therefore should also be capable of predicting in-core nuclear heating as a function of reactor power.