Quantifying a Common Inconsistency in RANS-VoFModeling 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 water-based Reynolds number, Re_w, are considered and solved via DNS. Symptoms of the inconsistencies include a lack of diffusivity in the average local oil fraction and 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. With the absence of diffusivity in mean oil fraction, knowledge about mean interface distribution is lost as well. From a momentum perspective, the more troubling issue is the absence of fluctuating terms associated with viscous and surface tension forces. For momentum advection, terms associated with fluctuating density can be safely ignored due to the similar magnitude between oil and water density.