A Mechanistic Model for Flooding in Vertical Tubes

In a counter-current two-phase flow system, flooding can be defined as the onset of flow reversal of the liquid component which results in an upward co-current flow. Flooding in the surge line of pressurized water reactors poses a significant technical challenge in the analysis of several postulated nuclear reactor accident scenarios. Despite the importance of flooding in these analyses, previous work does not identify a universally accepted rigorous physics-based model of flooding, even for the simple case of flooding in adiabatic, vertical tubes. This can be attributed to a lack of conclusive understanding of the physics of two-phase counter-current flow, specifically the mechanism of flooding, and the large amount of uncertainty among data from various flooding experiments. This deficiency in phenomenological and experimental knowledge has led to the use of many empirical and semi-empirical correlations for specific system conditions and geometries. The goal of this work is the development of a model for flooding in vertical, adiabatic tubes from first principles. To address a source of uncertainty in the analysis of flooding, a model for the prediction of average film thickness in annular co- and counter-current flows has been developed by considering the conservation of momentum of the liquid and gas flows. This model is shown to be a quantitative improvement over the most commonly used models, those of Nusselt and Belkin, Macleod, Monrad, and Rothfus. The new model better considers the effects of interfacial shear and tube curvature by using closure relations known to represent forces appropriately in co- and counter-current flow. Previous work based on semi-empirical flooding models has been analyzed to develop a new theory on the hydrodynamic mechanism which causes flooding. It is postulated that the growth of an interfacial wave due to interfacial instability results in a flow reversal to ensure that momentum is conserved in the counter-current flow system by causing a partial or complete co-current flow. A model for the stability of interfacial waves in a counter-current flow system is proposed and has been developed herein. This model accurately represents the geometric and flow conditions in vertical adiabatic tubes and has been shown to have limits that are consistent with the physical basis of the system. The theory of waves of finite amplitude was employed to provide closure to an unknown parameter in the new model, the wave number of the wave that generates the interfacial instabil- ity. While this model underpredicts the flooding superficial gas velocity, the result is a conservative estimate of what conditions will generate flooding for a system. In the context of the analysis of a nuclear reactor, specifically a pressurized water reactor, conservatism means that the gas flow rate predicted to cause flooding for a fixed liquid flow rate will be less than the flow rate found experimentally, mean- ing that liquid delivery to the core would be safely underestimated. Future work includes the improvement of the closure relation for the limiting wave number that will cause unstable interfacial waves, as well as an assessment of the applicability of the stability-based model to flooding in the presence of phase change and flooding in complex geometries.