Closure relations of the one-dimensional two-fluid model for the simulation of slug flows

Abstract

The present research is a development of an existing numerical methodology, based on a one-dimensional two-fluid model. This model is capable of simulating two-phase slug flow for horizontal and nearly horizontal pipes, using a slug capturing technique. However, the governing system of equations is known to be only conditionally wellposed. The main objective of the research is to extend the applicability of the model to a wider range of cases, through the introduction of various closure models, which aim to better describe the physics of the flow. The approach to the problem starts from a mathematical evaluation of additional relations for the equation system in order to study their contribution to the well-posedness of the problem by means of a characteristics analysis. A stability analysis provides information on the growth rate of the instabilities: if this growth rate is bounded for short wavelength instabilities the system can be considered well-posed. Among the closure relations studied and tested are those relating to the effects of surface tension, virtual mass (due to relative acceleration), shape of velocity profiles and axial diffusion. Suitable closure relationships are then implemented and tested in the numerical code and the results are validated against available experimental data for slug flows. For a successful improved model, numerical results must be both in good agreement with experiments and converge to the same solutions with grid refinement, which is a clear manifestation of the well-posedness of the system. The main advance made in this research project comes from the formulation, analysis and implementation of appropriate coefficients for the inclusion of diffusive terms in the mathematical and numerical model. It was found that these terms are able to render the system of equations well-posed and that the results of simulations are in good agreement with the experimental evidence for slug flow cases.