Assessment of closure relations on the numerical predictions of vertical annular flows with the two-fluid model

Abstract

In the present work, different closure relations in the one-dimensional Two-Fluid Model were investigated in order to assess the effect on the numerical simulation of vertical annular flows, including the formation and propagation of waves at the gas-liquid interface. Different interfacial friction formulations, momentum flux parameters and dynamic pressure terms were employed. The conservation equations were discretized and solved within the finite volume framework, with a first order time discretization, a second order TVD and first order Upwind schemes for the convective term. A rigorous mesh sensitivity analysis was performed, showing the advantages and shortcomings of each discretization scheme, as well as the impact of closure formulations and their importance for better physical representativeness and well-posedness. Flow and wave parameters were obtained with the different approaches for various test cases taken from the literature. A sensitivity analysis was performed with varying momentum flux parameter values, interfacial friction factors and dynamic pressure expressions. Liquid film thickness, pressure-drop and wave characteristics results were systematically compared to experimental data. Predictions for pressure gradient and mean liquid holdup with the best set of closures presented an average error of 9% and 22%. Comparison of the wave characteristics, given by the group speed and frequency with available measured values has shown that the model is capable to simulate the qualitative features of wave formation and propagation in vertical annular flow with a reasonable quantitative agreement, given the complexity of the physical phenomena involved. However, while it has been shown through the sensitivity analysis that the closure relations investigated here have an important effect on quantities of interest in annular flows, in particular that a momentum flux parameter value larger than unit seems beneficial, further investigations are suggested for a wider range of conditions, providing a robust physical support for the generalization of the closure model formulations.