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

A deterministic model for calculating the time dependent fission yield from solutions has been developed. The model is based on transient finite eleme nt methods and couples radiation transport modelling with computational flu id dynamics. Non-linear space dependent kinetic equations are derived, in w hich 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 neu tron precursor concentrations together with the energy fields. Applications focus on the role of radiolytic gas evolution and buoyancy induced fluid m otion on the criticality of fissile liquids with delayed and prompt supercr itical step reactivity insertions. The analysis is performed with uranyl ni trate solutions. The theory behind the modelling is presented, together with numerical resul ts, to validate the approach. The resulting computer code, which we call FE TCH (finite element transient criticality), is validated against point kine tics based models fur right cylinders and against experiment for both low ( delayed supercritical) and high powered (usually prompt supercritical) tran sients. The term 'low powered' in this context will be used to describe tra nsients in fissile liquids in which the rate of radiolytic gas generation i s so small that it can be ignored without sacrificing the accuracy of the s imulations. Modelling can then be conducted in a single fluid phase. The te rm 'high powered' refers to transients in which gas evolution and ensuing f ree surface motion play an important part in their dynamics and are thus so lved using the multi-phase mode of FETCH. The simulations presented here pr ovided extensive insights into the dynamics of these transients which can b e difficult to study in detail with experiment. (C) 2001 Published by Elsev ier Science Ltd. All rights reserved.