A method for simulating two-phase pipe flow with real equations of state

• A four-equation two-fluid model with instantaneous phase equilibrium is tested.
• The four-equation two-fluid model is compared with a five-equation two-fluid model.
• CO2 thermodynamic properties are described using the Span–Wagner equation-of-state.
• Robust transition from two-phase to single-phase flow is demonstrated.

Common two-fluid models for pipe flow assume local non-equilibrium regarding phase transfer. To solve the two-fluid models together with accurate equations of state for real fluids will in most cases require mechanical, thermal and chemical equilibrium between the phases. The reason is that reference equations of state for real substances typically describe full thermodynamic equilibrium. In this paper, we present a method for numerically solving an equilibrium model analysed by Morin and Flåtten in the paper A two-fluid four-equation model with instantaneous thermodynamical equilibrium, 2013.The four-equation two-fluid model with instantaneous thermodynamical equilibrium is derived from a five-equation two-fluid model with instantaneous thermal equilibrium. The four-equation model has one mass equation common for both phases, but allows for separate phasic velocities. For comparison, the five-equation two-fluid model is numerically solved, using source terms to impose thermodynamical equilibrium. These source terms are solved using a fractional-step method.We employ the highly accurate Span–Wagner equation of state for CO2CO2, and use the simple and robust FORCE scheme with MUSCL slope limiting. We demonstrate that second-order accuracy may be achieved for smooth solutions, whereas the first-order version of the scheme even allows for a robust transition to single-phase flow, also in the presence of instantaneous phase equilibrium.