Entropy consistent modeling of compressible two-phase flow in wide concentration range

The two-phase flows containing dispersed phase usually display distinct flow patterns in dense and dilute concentration regimes. The typical case is the high-speed droplet-laden gas flow, in which permanent contact between droplets exists only in the dense concentration regime. For such two-phase flows, various models have been proposed adopting the two-fluids approach. Among them, some are well acceptable for a single flow pattern; however, few are considered suitable for both. This work presents a new model for such mixture flows, applying to a wide concentration range. In the dilute regime, it corresponds to a conditionally hyperbolic model that has been extensively studied in the literatures, while in the dense regime, it corresponds to a symmetric extension of the well-known Baer–Nunziato model. The entire model is fully entropy consistent, total momentum, and energy conserving, while enabling a smooth transition from dilute to dense regime. Analysis is provided for its characteristic as well as asymptotic limits in stiff mechanical relations. Finite volume-type method for numerical solution is designed consistently by combining sharp interface resolving solvers for the dense and dilute flow patterns. A series of numerical tests are carried out to illustrate the capability and advantage of the new model and its solution method.