Non-linear space-dependent kinetics for the criticality assessment of fissile solutions

Abstract

A deterministic model for calculating the time dependent fission yield from solutions has been developed. The model is based on transient finite element methods and couples radiation transport modelling with computational fluid dynamics. Non-linear space dependent kinetic equations are derived, in which the non-linearities arise due to radiolytic gas generation, geometical changes in the liquid, the temperature dependent densities, cross sections and thermally/gas induced fluid motion. The latter advects the delayed neutron precursor concentrations together with the energy fields. Applications focus on the role of radiolytic gas evolution and buoyancy induced fluid motion on the criticality of fissile liquids with delayed and prompt supercritical step reactivity insertions. The analysis is performed with uranyl nitrate solutions. The theory behind the modelling is presented, together with numerical results, to validate the approach. The resulting computer code, which we call FETCH (finite element transient criticality), is validated against point kinetics based models for right cylinders and against experiment for both low (delayed supercritical) and high powered (usually prompt supercritical) transients. The term ‘low powered’ in this context will be used to describe transients in fissile liquids in which the rate of radiolytic gas generation is so small that it can be ignored without sacrificing the accuracy of the simulations. Modelling can then be conducted in a single fluid phase. The term “high powered’ refers to transients in which gas evolution and ensuing free surface motion play an important part in their dynamics and are thus solved using the multi-phase mode of FETCH. The simulations presented here provided extensive insights into the dynamics of these transients which can be difficult to study in detail with experiment.