Predicting the void fraction of a two-phase flow outside of tubes is essential to evaluate the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture properties and affects two-phase mixture velocity, which enable evaluating the pressure drop of the system. The two-fluid model for the numerical simulation of two-phase flows requires interaction laws between phases which are not known and/or reliable for a flow within a tube bundle. Therefore, the mixture model, for which it is easier to implement suitable correlations for tube bundles, is used. Indeed, by expressing the relative velocity as a function of slip, the void fraction model of Feenstra et al.and Hibiki et al. developed for upward cross-flow through horizontal tube bundles is introduced and compared. With the method suggested in this paper, the physical phenomena that occur in tube bundles are taken into consideration. Moreover, the tube bundle is modelled using a porous media approach where the Darcy–Forchheimer term is usually defined by correlations found in the literature. However, for some tube bundle geometries, these correlations are not available. The second goal of the paper is to quickly compute, in quasi-real-time, this term by a non-intrusive parametric reduced model based on Proper Orthogonal Decomposition. This method, named Bi-CITSGM (Bi-Calibrated Interpolation on the Tangent Subspace of the Grassmann Manifold), consists in interpolating the spatial and temporal bases by ITSGM (Interpolation on the Tangent Subspace of the Grassmann Manifold) in order to define the solution for a new parameter. The two developed methods are validated based on the experimental results obtained by Dowlati et al. for a two-phase cross-flow through a horizontal tube bundle.

Being able to predict the void fraction is essential for a numerical prediction of the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture density and affects two-phase mixture velocity which enable to evaluate the pressure drop of heat exchanger, the mass transfer and heat transfer coefficients. In this study, the flow is modelled by coupling Ansys Fluent with an in-house code library where a CFD porous media approach is implemented. In this code, the two-phase flow has been modelled so far using the Eulerian model. However, this two-phase model requires interaction laws between phases which are not known and/or reliable for a flow within a tube bundle. The aim of this paper is to use the mixture model, for which it is easier to implement suitable correlations for tube bundles. By expressing the relative velocity, as a function of slip, the void fraction model of Feenstra et al. developed for upward cross-flow through horizontal tube bundles is introduced. With this method, physical phenomena that occur in tube bundles are taken into consideration in the mixture model. The developed approach is validated based on the experimental results obtained by Dowlati et al.