Movement of Two Liquid Columns Separated by a Gas Pocket in a Perforated Nozzle of a Liquid Injection Shutdown System

Abstract

The design of a liquid injection shutdown system which has been considered for retrofitting in Pickering NGS A includes a pocket of helium gas trapped between two liquid columns in the injection nozzle and piping. The nozzle is a perforated vertical tube submerged in the liquid moderator inside the reactor calandria vessel. It is initially full of moderator. At the other end of the injection line, liquid poison is held in a tank. The piping between the two liquids is filled with helium to minimize the inertia of the system and to facilitate sufficiently fast delivery of pis011 solution into the core. At the start of the injection, high pressure helium is rapidly applied to the poison surface in the tank. As poison is pushed through the piping, it compresses the trapped gas and causes ejection of first the moderator fluid and later also the trapped gas through the holes in the nozzle into the ambient moderator. When the poison front reaches the first holes, poison starts being ejected. The process is very fast; the injection is completed in a few seconds. The main difficulty in analyzing this transient is due to the presence of two coupled moving boundaries, i.e., the interface between the moderator and the gas and the interface between the gas and the poison. These interfaces proceed through the perforated nozzle at changing speeds while both the gas and the liquids are being ejected into the ambient at variable rates depending on the local pressure differential. With the perforations modelled as a continuous slot, the problem is reduced to a single nonlinear partial differential equation of second order, parabolic in time and one-dimensional in space. It results from combining the continuity and momentum equations for the liquid and contains as the unknown function the axial velocity in the liquid column. The equation is defined on a variable interval between a fixed nozzle end and a moving liquid-gas interface. Coupled integration of the poison column movement in the piping and the trapped gas pressure transient provides the instantaneous boundary conditions for velocity at the fixed end and for pressure (and through it for the derivative of velocity) at the moving interface. The governing equation and the pressure boundary condition are common to both liquid columns; only the fixed-end velocities are different. When the gas pocket is entirely ejected, the two liquid columns merge smoothly into one. The same equation continues to govern the liquid movement in the nozzle and the liquid ejection rates; however, this time it is defined on a fixed domain representing the whole nozzle, with velocities known at both ends. A simple coordinate transformation is used to turn the problem with a moving boundary into one defined on a fixed domain (the unit interval in the computational space) with slightly different coefficients in the equation. The solution is obtained by means of an implicit, second-order finite-difference scheme which leads to a tridiagonal system of algebraic equations. The numerical results include a comparison between two options of the nozzle design. The pressure transients experienced by the trapped gas are physically sensible.