Stability of natural circulation boiling water reactors: Part I - Description stability model and theoretical analysis in terms of dimensionless groups

A theoretical model describing coupled neutronic-thermohydraulic power oscillations in natural circulation boiling water reactors (BWRs) is developed. The governing equations for the thermohydraulic subsystem are transformed to a dimensionless basis, to eliminate all explicit pressure dependence in the model. It is proved that all necessary information about the operating conditions is incorporated in only two dimensionless numbers: the Zuber and the subcooling number. The density ratio number cancels in the dimensionless equations because a homogeneous flow model is applied. The Froude number is also shown to be redundant in a natural circulation system, as it can be expressed in the other dimensionless groups. The stability boundary of the complete coupled neutron ic-thermohydraulic reactor system in the dimensionless Zuber-subcooling plane is estimated to be rather insensitive to the system pressure as well. Therefore the usage of dimensionless stability maps, instead of the traditional power-flow maps, is strongly recommended as an efficient method to determine the dynamic characteristics of natural circulation BWRs.