Numerical Simulation of Weakly Compressible Multiphase Flows with a Baer-Nunziato Type Model

We present the results of the simulation of two-phase CO2 flows at low-Mach number, obtained through a pressure-based Baer-Nunziato type model. The underlying full non-equilibrium model enables the description of each phase with its own thermodynamic model, so it circumvents the requirement of the definition of the speed of sound of the vapor-liquid mixture. The primitive formulation, combined with a special pressure scaling to correctly capture the behavior in the zero-Mach limit, is well-suited to model weakly compressible flows, and makes easier the use of arbitrary thermodynamic models. At the interfaces, the phasic velocity and pressure are driven toward the equilibrium by means of relaxation processes, whose velocities are controlled by user-defined parameters. The set of seven partial differential equations describing the flow evolution is discretized through a finite-volume scheme in space and an hybrid implicit-explicit time discretization, to avoid the stringent time step limitation imposed by the acoustics. We compare the results of a shock-tube problem, initially containing saturated CO2, obtained according to the stiffened gas model and to the Peng-Robinson equation of state.