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— The subject of multiphase flow encompasses a vast field hosting different technological contexts, wide spectrum of different scales and broad range of engineering disciplines along with multitude of different analytical approaches. A persistent theme throughout the study of multiphase flow is the need to model and predict the detailed behavior of such flow and the phenomenon it manifests. In general, there are three ways to explore the models of multiphase flow: (1) Develop laboratory-sized models through conducting lab experiments with good data acquisition systems; (2) Advance theoretical simulations by using mathematical equations and models for the flow; and (3) Build computer models through utilization of power and size of modern computers to address the complexity of the flow. While full-scale laboratory models are essential to mimic multiphase flow to better understand its boundaries, the predictive capability and physical understanding must depend on theoretical and computational models. Such a combination has always been a major impediment in the industry and academia. Different numerical methods and models with dissimilar concepts are being conveniently used to simulate multiphase flow systems depending on different concepts. Some of these methods do not respect the balance while others damp down strong gradients. The degree of complexity of these models makes the solution practically not reachable by numerical computations despite the fact that many rigorous and systematic studies have been undertaken so far. The essential difficulty is to describe the turbulent interfacial geometry between the multiple phases and take into account steep gradients of the variables across the interface in order to determine the mass, momentum and energy transfers. NASA-VOF 3D is a transient free surface fluid dynamics code developed to calculate confined flows in a low gravity environment using the Volume of Fluid (VOF) algorithm. In this study, theoretical investigation has been carried out to better understand the impact of a horizontal bend on incompressible two-phase flow phenomenon. NASA-VOF 3D has been considered as the CFD platform for major modifications carried out to the main two governing equations; namely the Continuity (Mass Conservation) and the Momentum (Navier-Stokes) equations using the Volume of Fluid (VOF) algorithm. The modifications consisted of deriving and developing the governing equations needed to reflect the impact of the bend on the transition. Numerical operators have also been developed to gain better convergence during calculations. This paper presents the details of this theoretical and numerical study and the derivations of the modified governing equations.

Theoretical Investigation to Develop a Fit-for-purpose CFD Code to Simulate Transient Incompressible Two-phase Flow