On the levitation force in horizontal core-annular flow with a large viscosity ratio and small density ratio

Abstract

A numerical study has been made of horizontal core-annular flow: the flow of a high-viscosity liquid core surrounded by a low-viscosity liquid annular layer through a horizontal pipe. Special attention is paid to the question how the buoyancy force on the core, caused by a density difference between the core and the annular layer, is counterbalanced. The volume-of-fluid method is used to calculate the velocities and pressures in the two liquids. At the start of the calculation the core is in a concentric position. Thereafter the core starts to rise under the influence of buoyancy until it reaches an eccentric equilibrium position where the buoyancy force is counterbalanced by hydrodynamic forces generated by the movement of a wave at the core-annular interface with respect to the pipe wall. At high Reynolds number of the flow in the annular layer core levitation is due to inertial forces, whereas at low Reynolds number viscous (lubrication) forces are responsible for levitation. We carried out two types of calculation. In the first we assume the interface to be smooth (without wave) at the start of the calculation and study how the wave develops during the rising period of the core. In the second a wave is already present at the start of the calculation.

CFD simulation of interfacial instability from the nozzle in the formation of viscous core‐annular flow

“…The wave evolution presented high wave amplitude which the core was destabilized forming a structure of OSTW. The initial formation of waves at the pipe top with the smooth interface at the bottom has been reported by Ooms et al, where the oil velocity is U o = U w with a high viscosity of µ o = 0.601 Pa · s and oil core density of ρ o = 980 kg · m −3 . The high wave amplitude and short wavelength were found in theoretical and experimental studies by Joseph et al and Sotgia et al using water input fractions between C w = 0.2 and C w = 0.06, respectively.…”

“…An extensive study of mathematical modelling has been used with an empirical input interface structure assuming a shape of the wave such as: sawtooth wave, snake waves, and smooth interface with a concentric solid core. Computational fluid dynamics have been applied to calculate the turbulent annular flow using the k‐ϵ model with laminar viscous oil, and for two‐phase modelling .…”

A comparison between numerical predictions and theoretical and experimental results for laminar core‐annular flow

“…As shown by Ooms et al 5 the waves can generate a downward force (due to a pressure buildup at the top of the pipe) that counterbalances the upward buoyancy force in horizontal core-annular flow in case of a smaller density of the core liquid than the density of the annular liquid, thus making a stationary flow possible. In that case, the core will get an eccentric position in the pipe due to the buoyancy force and the waves will become less symmetric in the longitudinal direction of the pipe and also nonaxisymmetric (for more details see Ooms et al 5 ).…”

“…We found the same result. The details of this study are reported in Ooms et al 5 We have extended this calculation by studying the influence of the initial conditions by changing these conditions while keeping the physical parameters, the computational mesh, and the time step restriction the same as in the foregoing calculation. We studied two different initial conditions.…”

“…More details about the results of linear stability calculations for the growth of waves at the interface (and about the effect of interfacial tension) are given by Li and Renardy. 4 It has been shown that laminar core-annular flow (high-viscosity core, laminar low-viscosity annular layer) can be simulated by means of numerical calculations using the volume-offluid method, see Li and Renardy 4 and Ooms et al 5 In these articles, the validation of the method against theoretical results (of linear stability calculations) and experiments is somewhat limited. Therefore, we have extended this validation significantly for the case of vertical (upward) laminar core-annular flow and the results are presented in this article.…”