Lubricated pipelining: stability of core-annular flow

Abstract

The stability of core-annular flow (CAF) in pipes is analysed using the linear theory of stability. Attention is confined to the potentially stable case of lubricated pipelining with the less viscous liquid, say water, in the annulus. The effects of surface tension and density are included, but gravity is excluded. We find upper and lower branches of the neutral curve in a Reynolds number (ℝ) vs. wavenumber (α) plane. A window of parameters is identified in which CAF is stable to small disturbances. When ℝ is below the lower critical value, CAF is destabilized by surface tension and long waves break up into slugs and bubbles. The sizes of slugs and bubbles of oil in water observed by Charles, Govier & Hodgson (1961) are given by the wavelength of the fastest growing long wave. This long-wave instability is a capillary instability, modified by shear, which reduces to Rayleigh's instability in the appropriate limit. At higher ℝ, the capillary instability is stabilized by shear. At yet higher ℝ, above the upper critical value, the flow is unstable to generally shorter waves which leads to emulsification, water droplets in oil. The theory agrees with experiments. The analysis seems to be applicable to the design of lubricated pipelines; for example, there is an optimum viscosity ratio for stability, greater stability can be obtained by using heavy liquid as a lubricant when the flow is unstable to capillary modes on the lower branch and by using light liquids when the flow is unstable to emulsifying disturbances on the upper branch.

Stability of axisymmetric core–annular flow in the presence of an insoluble surfactant

“…The discrepancy was resolved by noting a crossover in the growth rates when the capillary number is increased from zero. Neutral curves for a fixed suitably defined surface tension parameter and varying Reynolds or capillary number reproduced previous results of Preziosi et al (1989) for a clean interface, and extended them to non-zero Marangoni numbers. In the presence of a mean flow, a long-wave instability occurs at small Reynolds numbers.…”

“…At higher values of Ca, the growth rates for a contaminated interface are larger than those for a clean interface. Preziosi et al (1989) performed a linear stability analysis for a clean interface and presented neutral curves for fixed values of J . In figure 8, we display with the broken line the neutral curve obtained when J = 1.0695 × 10 5 , λ = 0.1, a/b = 0.8696 and Ma = 0, which corresponds to the conditions used to produce their figure 8.…”

“…In both parts of the present study, axisymmetric disturbances are also considered. However, the severity of this restriction is ameliorated by the discovery that axisymmetric modes are known to be most dangerous for a clean interface (Preziosi, Chen & Joseph 1989). The numerical results will show that the primary destabilizing effect of the surfactant is to extend the range of unstable linear modes to a wider range of wavenumbers.…”

Linear stability analysis and numerical simulation of miscible two-layer channel flow

“…These have included linear stability analyses for horizontal [6,7,[17][18][19] and vertical pipes [5,20], accounting for viscosity and density contrasts, experiments [21,22] and numerical simulations in straight [9,10,23] and corruagated pipes [24][25][26][27].…”

Applying CFD in the analysis of heavy oil - water two-phase flow in joints by using core annular flow technique

“…Bentwich et al [22] studied the eccentric annular flow, for the oil core and water pellicle flowing in laminar regime. The volumetric flow of two immiscible fluids was obtained by integrating the velocity profiles, in a horizontal pipe with a circular and eccentric interface.…”