A four-equation two-phase flow model for sodium boiling simulation of LMFBR fuel assemblies

Abstract

A three-dimensional numerical model for the simulation of sodium boiling transients has been developed. The model uses mixture mass and energy equations, while employing a separate momentum equation for each phase. Thermal equilibrium on the saturation line between coexisting phases is assumed.

The four governing equations are supplemented by a number of constitutive relations, addressing the interphase and intraphase exchanges, as well as the fluid-solid interactions. It should be noted that this four-equation two-phase flow model requires only one interfacial relation, i.e., the momentum exchange, compared to the six-equation model which needs two additional relations, describing the mass and energy exchanges. Consequently, the relatively high degree of uncertainty currently associated with the interfacial exchange phenomena is considerably reduced.

From a numerical point of view, the basic approach in this work is a semi-implicit method, in which pressure pulse propagation and local effects characterized by short characteristic times are treated implicitly, while convective transport and diffusion heat transfer phenomena, associated with longer time constants, are handled explicitly. The method remains tractable and efficient in multidimensional applications.

Simulation of a number of experiments has yielded very encouraging results. The numerical method and the constitutive relations have performed well, especially so in light of the extreme severity of the conditions involving sodium boiling.