Terrestrial Systems Ecology Group

Dokhane Abdelhamid - Analytical Modelling and Nonlinear Stability Analysis of Boiling Water Reactors

From the physical point of view, Boiling Water Reactor (BWR) stability behaviour is a very complex phenomenon. Although extensive research has been carried out in recent years, the phenomenon is not yet completely understood. These instabilities were identified as diverging or self-sustained oscillations of the neutron flux. Global and regional power oscillations are characteristic of the dynamic behaviour of a BWR, in which a strong nonlinear coupling between the neutronic and thermal-hydraulic processes exists via void feedback reactivity.

Because of the large computational effort required, large system codes cannot in practice be employed for a detailed investigation of the complete manifold of solutions of the nonlinear equations describing the BWR system, and thus the so-called reduced order models become necessary. Such models contain a minimum number of system equations describing the physical phenomena of interest with adequate sophistication, but the geometrical complexity is reduced by only modelling a few channels. Their foreseen application is to provide a new and deep insight into the physical mechanisms underlying the neutronics/thermal-hydraulics induced power oscillations in BWRs. The main advantage of employing reduced order models is the possibility of using semi-analytical methods for performing bifurcation analysis. In such an analysis, the stability properties of a fixed point, or a limit cycle, are investigated analytically without the need for solving the system of differential equations explicitly.

This doctoral research, conducted in the framework of a collaboration between PSI and EPFL in the field of reactor physics, contributes to the in-depth understanding of the physical mechanisms of neutronics/thermal-hydraulic instabilities, in particular from the nonlinear point of view using modern bifurcation analysis. Thus the research serves to clarify the conditions under which such instabilities can occur in BWRs. For this purpose, a more complex analytical model has been developed employing an appropriate set of nonlinear differential equations, the solution manifold for which will have to be examined thoroughly. For example, if for a certain system parameter set, sub- or supercritical Hopf bifurcation exists; the stability behaviour of this operational point is analysed in greater detail using the systems code RAMONA. Thus, one the main objectives of the thesis is to understand the systems code solutions on the basis of the physical mechanisms identified in the course of the sophisticated reduced-order model analysis.