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

This research is a development of an existing numerical methodology (Issa and Kempf, 2003,
based on a one-dimensional two-fluid model.
This model is capable of simulating two-phase stratified and slug flow for horizontal and nearly horizontal pipes, using a novel "slug capturing" technique. However, the governing
system of equations is conditionally well-posed only.The main objective of the research is to extend the applicability of the model to a wider range of cases.
This can be achieved through the introduction of improved closure models, which aim to better describe the physics of the flow. The approach to
the problem starts from a mathematical evaluation of the additional closure relations in order to study their contribution to the well-posedness of the system.
On one hand a characteristics analysis stablishes whether the characteristics of the problem are real, hence the system is hyperbolic and well-posed. On the other hand 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 axial diffusion,
surface tension, virtual mass (due to relative acceleration) and shape of velocity profiles.
Suitable closure relationships are then implemented and tested in the numerical code and the results are validated against available experimental data.
For a successful improved model, numerical results must be both in good agreement with
experiments and grid independent, which is a clear manifestation of the well-posedness of the system. These factors were used to evaluate the performance of the new models.