A novel modeling method for the interfacial instability of immiscible fluids along ducts

Daniel Rodriguez¹

¹ Pontifícia Universidade Católica de Rio de Janeiro

doi:10.20906/CPS/COB-2015-0492

Resumo

Most methods used presently in the oil extraction and chemical processing industries for the fast prediction and modeling of interfacial instabilities in confined two-phase flows are based on the so-called two-fluids model, which was developed more than three decades ago. This mechanistic model simplifies the problem by averaging the flow over the cross-section, thus assuming constant velocity profiles and introducing heuristic correlations for the friction factors. Conversely, more fundamental methods for understanding the physics based on variations of the Orr-Sommerfeld equation (e.g. Boomkamp et al. 1997) have not been developed further due to their higher associated computing expenses. This paper presents a novel methodology for the computation of confined two-phase flows with interfacial instability. The improved capabilities of present-day computers and algorithms allow us to eliminate the strong simplifications of the two-fluids model and define a problem from first-principles in which the velocity profiles as well as friction factors are computed as part of the solution. A combination of the parabolized Navier-Stokes equations and parabolized stability equations with an interface-capturing scheme analogous to the level-set method are solved using sparse linear algebra and shared-memory parallelization. The proposed method is shown to be able of computing the unsteady velocity field associated with interfacial waves in an oil-water channel flow in few minutes on a laptop computer.

Palavras-chave: Two-fluid shear flows; Interfacial waves; Parabolized Navier-Stokes equations; Parabolized Stability Equations