A suitability analysis of transient one-dimensional two-fluid numerical models for simulating two-phase gas-liquid flows based on benchmark problems

Gas-liquid two-phase flows in pipes are present in a variety of engineering applications. These applications require transient one-dimensional mathematical models coupled with robust numerical methods to simulate the flow behavior in time and space. As there exist several possible combinations of models and numerical methods, questions arise as to the suitability of these numerical models to best accommodate the problem features. Aiming to partially answer this question, we present in this work numerical simulations of two well-known gas-liquid benchmarks, the water faucet, and the shock tube problems, carried out with two two-fluid models - 4E1P (four equations and one pressure) and 5E2P (five equations and two pressures) - in association with three numerical methods - FCT (Flux-Corrected Transport method), FORCE (First-Order Centered Scheme) and ModFORCE. The numerical methods used herein are written in a general form and do not require the solution of the associated Riemann problem. The obtained results are sought to serve as a reference to choose the best approaches, among the ones studied, to tackle some transient one-dimensional two-phase flow problems, highlighting the advantages and disadvantages of each model and method combination regarding hyperbolicity, diffusive and dispersive effects. Overall, the combination of the 5E2P model with the ModFORCE numerical method provides the most accurate results compared to the analytical solutions available.