Development of a four-fluid model for condensing steam flows

Highlights: • A novel four-fluid model is proposed to model condensing water-steam flows for a wide variety of flow conditions. • The four-fluid model is derived based on the two-fluid model, and expands upon the existing three-fluid model for vapor, liquid film, and entrained droplets. • The model requires twelve field equations, with twenty closure relations to address interfacial interactions, wall boundary conditions, and equations of state. • A comparison is demonstrated between the three-fluid and four-fluid model for the possible event of overflow into a nozzle geometry. A new four-fluid model is proposed for condensing water-steam flows applicable to a wide variety of different flow conditions relevant for nuclear power plants. The model expands upon current state-of-the-art three-fluid models by adding a second droplet fluid phase to account for homogeneous nucleation of droplets from the bulk vapor field. Consistent with prior three-fluid models, liquid wall film and entrained droplet fluids share a common temperature and energy equation, resulting in a system of eleven conservation equations. An additional governing PDE is required for the nucleated droplet number density, for twelve total governing equations. A full set of closure relations for the interphase and wall interactions is given. An initial test of the model formulation in a quasi-one-dimsensional converging-diverging nozzle with condensing steam was carried out using a simple in-house solver as a proof of concept. Results showed qualitatively correct trends compared with experimental data.