The classic four-equation drift-flux model treats the two-phase flow as a mixture to formulate mass, momentum, and energy balance equations. The dispersed phase is modeled in the mass balance equation to describe the mass transfer between the two phases. However, this model implies an assumption of the thermal equilibrium in the mixture energy balance equation. Therefore, a five-equation drift-flux model and its constitutive equations have been developed to relax the thermal equilibrium assumption in the classic four-equation drift-flux model when it is applied to thermal non-equilibrium phenomena in Light Water Reactors (LWRs). The additional energy balance equation of the dispersed phase has been introduced to address thermal non-equilibrium phenomena in LWRs in the five-equation drift-flux model. In addition, the newly added energy equation for the dispersed phase does not change the basic kinematic parameters and uses the mixture velocity instead of the dispersed phase velocity.

The hyperbolicity of the drift-flux model system equations is investigated by examining if the partial differential equations have only real eigenvalues. The results show that the five-equation drift-flux model is a well-posed hyperbolic model, which can be solved by both advanced solvers using the finite element method, such as MOOSE Framework, and the traditional solvers using finite difference method, such as RELAP5 code.

In developing the thermal non-equilibrium five-equation drift-flux model, it is necessary to select, improve, or develop constitutive models as closure relations for variables used in the field equations. In our current study, a literature survey has been conducted to review appropriate constitutive models and correlations for the dispersed phase mass generation rate, interfacial energy transfer, distribution parameter, and drift velocity in the five-equation drift-flux model.

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