A Space-Time Reactor Simulation

Abstract

<p>Exploration of the processes involved in fission reactor dynamics and the solution techniques required for such a problem is the objective of this research. Reactor behavior is governed by neutron kinetics and thermalhydraulics, and the spatial and temporal interaction of the two processes. The analytical solution of such a problem in all but the simplest of cases, is impossible. Hence, numerical methods are required. Simulation software is developed to model the space-time behavior of nuclear systems and this software is then used to study the behavior of these systems. This investigation involves the mathematical modeling and numerical simulation of the phenomena encountered. The desired result is an accurate depiction of reactor behavior.</p> <p>The majority of contemporary simulations involve only a loose coupling between the neutronics and thermalhydraulics both spatially and temporally. It is more expedient to solve reactor kinetics and thermalhydrauluc simulation problems sepatately. A point kinetics model is frequently added to thermalhydraulic simulation to model reactor power but this would ignore spatial effects. The simultation developed here is a space-time reactor kinetics simulation with an integral thermalhydraulics module. This integral thermalhydraulics module provides for good spatial and temporal coupling of the two processes and is the primary distinguishing feature of the software.</p> <p>The rate form of the equation of state is used in the solution of the pressure field in the thermalhydraulic problem. A rate equation is better suited to the problem procedure for the thermalhydraulics than the use of an equation state.</p> <p>Efforts were made to take advantage of the structure of the problem to reduce computational effort. Partitioned matrices are used in the time integration of both the neutron kinetics and thermalhydraulics. This helped reduce computational effort by facilitating the use of routines that exploit the sparsity of the Jacobian. A second order semi-implicit Runge-Kutta method is used for the time integration of the neutron kinetics problem. This method requires matrix inversion but is a robust and reliable method for solving a stiff system of ordinary differential equations.</p> <p>The two component modules of the software, the neutronics and the thermalhydraulics, were developed and tested separately before they were integrated. The results of these tests and simulations using the completed software are given.</p>