# Development of a reduced-order model to investigate global/regional/local oscillations in BWRs and study of new stability indicators

[Rapport]

This report presents the results of some investigations performed at Chalmers University of Technology within the Nordic Thermal-Hydraulic Network (NORTHNET) in the area of stability of Boiling Water Reactors (BWRs). Such systems are known to pos- sibly become unstable under certain conditions, and thus the characterization of their stability properties is of prime importance. Due to the complexity of the problem at hand, a Reduced-Order Model (ROM) was developed, as an alternative to using three- dimensional solvers. The main advantage of using a ROM is that ROMs represent fast running models aimed at catching in a qualitative manner the physical phenomena of im- portance. In addition, the relative simplicity of ROMs compared with three-dimensional solvers leads to the possibility of providing some physical insight into the stability mech- anisms. The ROM developed in this project is unique since it has the ability to model global, regional, and local oscillations, and it is based on four heated channels. The four heated channels are necessary to properly represent the possible excitation of the two first azimuthal modes in case of regional oscillations. A careful examination of the ROM demonstrated that the stability behavior of the system is entirely defined by so-called Cmn-coefficients (assuming that there is no pure density wave oscillation). These coefficients represent the effect of a change of the void fraction on pairs of eigenmodes of the nuclear core. When these coefficients are positive, the system is clearly unstable because of the corresponding positive void feedback. When negative, it was demonstrated, both using the developed ROM and SIMULATE-3K, that the system becomes less stable for Cmn coefficients becoming more negative. A closer examination of the dependence of the Decay Ratio (DR) on the Cmn coefficients using the ROM also demonstrated that for small negative values of the coefficients, a non-monotonic relationship between the DR and the Cmn coefficients exists. Nevertheless, for realistic values of the void reactivity feedback, such a non-monotonic behavior cannot be noticed, because the Cmn coefficients are sufficiently negative. As a consequence, the estimation of the Cmn coefficients opens up the possibility of using such coefficients as a qualitative measure of core stability in a predictive manner. This could be used for instance as a means to compare the relative stability of several core loadings without the need of running lengthy time-dependent three-dimensional core calculations, and could be of great help to nuclear engineers when designing cores.

**Nyckelord: **boiling water reactor stability, decay ratio, space-dependent neutron noise, reduced order models, density wave oscillations

Denna post skapades 2013-02-18. Senast ändrad 2015-03-30.

CPL Pubid: 173758