A model for the momentum flux parameters of the 1D Two-Fluid Model in vertical annular flows: Linear stability and numerical analysis

The 1D Two-Fluid model is based on an area average process of the time and phase averaged Two-Fluid conservation equations to render the model tractable for industrial scale problems. Due to the averaging processes, the loss of information renders the standard model ill-posed for certain configurations, i.e., short wavelengths disturbances are amplified at an unbounded rate and unphysical solutions are obtained. Closure relations play a key role in this problem, since they are required to close the 1D system and they reintroduce missing physical parameters that may stabilize the flow and render the model well-posed. Two formulations for the liquid momentum flux parameter ($C_L$) for vertical annular flows are proposed based on local velocities distributions. Differential viscous Kelvin-Helmholtz and von Neumann stability analyses are performed to evaluate the proposed $C_L$ formulations and three dynamic pressure models. Results have shown that dynamic pressure closure models introduce a small additional amount of damping into the growth rate curves, without a significant change in the hyperbolicity of the system. On the other hand, the novel $C_L$ models can guarantee well posedness of the linear system by introducing a growth rate plateau, blocking the unbounded growth of instabilities. Numerical simulations were also performed, and numerical dispersion relations were extracted from the results showing good agreement against LST data, validating the methodology. The novel $C_L$models are evaluated against a large experimental database from the literature, showing that the proposed models outperform the standard constant $C_L$ values for both pressure drop and liquid film thickness.