Quantifying a common inconsistency in RANS-VoF modeling of water and oil core annular flow

Current trends in modeling CAF of oil and water combine the interface capturing methodology of VoF with the computational savings of a RANS approach. As demonstrated mathematically, this results in an inconsistency in the overall RANS-VoF treatment and incurs a number of omissions in the solution of oil fraction advection and momentum. To quantify these inconsistencies, five CAF cases with increasing $R{e}_w$ are considered and solved via DNS. Symptoms of the inconsistencies include qualitative errors in the prediction of the flow behavior in the entrance and fully-developed regions, as well as in the transition between these two regions. From a momentum perspective, the more troubling issue is the absence of unclosed terms resulting from fluctuating viscous and surface tension forces in the RANS equations. For momentum advection, terms associated with fluctuating density can be safely ignored due to the similar magnitude between oil and water density.