Two scale Two-Fluid Model

Stability analyses are performed on a new two-mode formulation of the incompressible variational Two-Fluid Model (TFM) [A. Clausse, and M. Lopez de Bertodano, Physics of Fluids 33: 033324, 2021]. The Zuber-Findlay drift flux variables, i.e., the volumetric flux and the drift flux, are used. The two resulting momentum equations are a short wave equation for the Drift Flux describing void waves and the well-known long wave Drift-Flux Model (DFM). A dispersion analysis performed with this decomposition shows that the instabilities decouple into local and long wavelengths respectively. The analysis of the wave equation demonstrates that the inertial coupling and a slug flow drag correlation make the model well-posed dispersive and slug wave unstable because of a kinematic instability. A new two-phase kinematic condition is derived and nonlinear simulations result in pulse waves. Finally, simulations of the long-wave density wave instability with and without slug waves are performed to illustrate the two-scale capability of the current two-mode TFM.