Hyperbolicity of One-Dimensional Two-Fluid Model With Interfacial Area Transport Equations

Two-fluid model with an empirical flow regime concept is widely used for two-phase flow analyses but suffers from its static and often non-hyperbolic nature. Recently, an interfacial area transport equation (IATE) has been proposed within the framework of the two-fluid model to dynamically describe the interfacial structure evolution and model the interfacial area concentration with the ultimate goal of modeling flow regime transition dynamically. Studies showed that the two-fluid model with the IATE (termed “two-fluid-IATE model” hereafter) could provide a more accurate prediction of the phase distributions and therefore improve the predictive capability of the two-fluid model. The inclusion of the IATE in the two-fluid model, however, brings about a subject of concern, namely, the well-posedness of the model. The objective of the present study is to investigate the issue of the hyperbolicity of a one-dimensional two-fluid-IATE model by employing momentum flux parameters, which take into account the coupling of the void fraction (volumetric fraction of the dispersed phase) and radial velocity distributions over the cross section of a flow passage. A characteristic analysis of the partial differential equations of the one-dimensional two-fluid model and two-group IATEs for an adiabatic flow was performed to identify a necessary condition for the system to achieve hyperbolicty. A case study was performed for an adiabatic liquid-liquid slug flow and the analysis showed that the hyperbolicty of the two-fluid-IATE model was guaranteed if appropriate correlations of the momentum flux parameters were applied in the two-fluid-IATE model.