Multi-Dimensional Modeling of Two-Phase Flows in Channels and Pipelines
Authors: Subramani Hariprasad , Kiara Areti , Campbell Bryce , Hendrickson Kelli , Liu Yuming 
Published: May 2013

Abstract
Two-phase flows in channels and pipelines involve complex multiscale dynamical processes such as interfacial wave growth due to flow instabilities, wave breaking and mixing, violent slugging, etc. This work describes a collection of three efficient, and physics-based, complementary numerical techniques that are developed to effectively address these nonlinear processes at different scales. In particular, these algorithms are used to study nonlinear interfacial wave interaction effects on flow transition and to develop physics-based turbulence closure models for simulating mixing and slug flows.
The first algorithm is a highly efficient two-dimensional viscous-potential flow method which is used for the simulation of large-scale nonlinear flows in horizontal channels and pipes for which the length (L) and height (D) ratio could reach L/D = O(10,000). This provides an effective capability for simulating the initiation and nonlinear evolution of interfacial disturbances and can be an aid in developing improved slug transition criteria. The second algorithm builds on the first capability by addressing the effects of flow vorticity and pipe inclination. This facilitates the prediction of occurrence conditions for flooding, backflow, and liquid slugging in inclined pipes.
The final method carries out direct numerical simulations of the Navier-Stokes equations (as well as large eddy simulations) allowing for the turbulent evolution of violent two phase flows to be examined. Such a method is limited to laboratory scale problems where L/D=O(1–10) and Re~O(50,000); however, all of the physical scales can be accurately resolved (either directly or through sub-grid scale models) allowing for robust turbulence closure models to be developed for interfacial and wall bounded flows.
By utilizing these three complementary numerical methods, a detailed understanding of the nonlinear evolution of two phase channel/pipe flows is obtained, enabling the development of physics-based turbulence closure models as well as nonlinear flow transition criteria for the prediction of large wave and slug formation.

Background
The formation and nonlinear evolution of slugs in pipelines represents a significant theoretical and numerical challenge as it involves the complex interaction of multiple processes which occur over a large range of scales. The dependence on long oil pipelines has produced continued interest in understanding the formation and nonlinear transition of small waves into large wave disturbances and slugs. The presence of these classes of flows creates significant flow assurance challenges and being able to consistently and accurately predict the conditions of slug flow remains an active area of research.
The theoretical prediction of slug flow is generally based on linear stability analysis of a stratified two-fluid state to an unstable slug flow state. Numerous stabilities models such as those by Taitel & Dukler (1976), Lin & Hanratty (1986), Barnea & Taitel (1993), and Funada & Joseph (2001) have been developed; however these models contain a wide range of physics which leads to large variations in the stability predictions between the various models. Being able to identify the key processes involved in the transition as well as the relevant interaction scales may improve the stability predictions.