Levitation of Core Flows

Abstract

A simple model is proposed for a 2D horizontal core annular flow in which the effect of gravity due to the difference in the densities of the two fluids is the eccentricity of the core. We split the domain through the center of the core; we characterized each sub domain by means of local variables, for instance the holdup ratio. We found that the smallest global pressure drop is achieved if and only if the local holdup ratios are equal to the global holdup ratio (for a perfect core annular flow this only happens when the core is centered). We used this result in a direct simulation of spatially periodic 2D wavy core annular flows carried out under the assumption that the viscosity of the oil core is so large that it moves as a rigid solid which may nevertheless be deformed by pressure forces in the water. The waves that develop are asymmetric with steep slopes in the high pressure region at the front face of the wave crest and shallower slopes at the low pressure region at lee side of the crest, as Bai et al. describe (1996). However two new issues are confronted in our 2D simulation. First, the shape and length of the upper and lower waves are different. Second, the displaced 2D core can be thought to represent eccentricity. We conclude that a positive pressure force is required to levitate the core off the wall when the densities are not matched and that the difference in the upper and lower wave shapes restore the effect of the eccentricity by allowing the local holdup ratios to be equal to the global holdup ratio; thus the pressure drop is the smallest possible.