Solution of Governing Equations for Six-Field System Code

Abstract

Modeling of two phase flows in nuclear power plants is very important for design, licensing, and operator training and therefore must be performed accurately. As requirements have increased, the form and accuracy of the models and computer codes have improved along with them. Early formulations for the field equations include: single phase liquid with algebraic drift flux for the gas phase, modeled with mass, momentum and energy governing equations; and two separate fields, liquid phase and gas phase, typically modeled with six governing equations. These lump bubbles and droplets into the gas and liquid phases respectively and use flow regime maps based upon available experimental data. However, the experiments do not cover the entire spectrum of reactor conditions, so that transitions and extrapolations, which are inherently inaccurate, must be employed. Further, some reactor scenarios, such as boiling and condensation, can be more accurately resolved by modeling bubbles or droplets separately from the continuous fields. Introduction of an additional field, droplet or bubble, apart from the continuous liquid and gas fields, generally uses nine governing equations. Despite the successful development of the above-mentioned methods for modeling reactor coolant flow in modern software, such as RELAP, TRAC, TRACE, CATHARE and many others, there remain reactor scenarios that require greater resolution to model. This is particularly true of conditions during reflood, where emergency spray flows dominate the cooling profile within the core. Existing system codes use a lumped approach for two phase flows that groups the fields by their phase, thereby losing track of the physical interactions between the discrete fluid fields. The accuracy of these accident analysis system codes can be improved by characterizing the interactions between additional coolant fields. To capture the effect of the various field interactions, governing equations involving six-fields have been developed. The six fields are 1) continuous liquid, 2) continuous vapor, 3) large droplets, 4) small droplets, 5) large bubbles and 6) small bubbles. The additional fields and the related governing equations introduce additional variables and source terms that require new closure relationships and primary variables. This article presents the equations and variables and develops the discrete set of 18 equations that must be solved to model the system.