Phase-field simulation of core-annular pipe flow

Abstract

Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical geometries is not established. We here quantitatively investigate the convergence of the phase-field method to the sharp-interface limit with simulations of two-phase pipe flow. We focus on core-annular flows, in which a highly viscous fluid is lubricated by a less viscous fluid, and validate our simulations with an analytic laminar solution, a formal linear stability analysis and also in the fully nonlinear regime. We demonstrate the ability of the phase-field method to accurately deal with non-rectangular geometry, strong advection, unsteady fluctuations and large viscosity contrast. We argue that phase-field methods are very promising for quantitatively studying moderately turbulent flows, especially at high concentrations of the disperse phase.

Direct numerical simulation of two-phase pipe flow: influence of the domain length on the flow regime

“…Additionally, we show that under these conditions, relaying in the predictions of the linear stability analysis of the initial CAF leads to a pipe length that is too short to capture the final state. While in some cases it might be a reasonable approach when the system tends to converge into a regime closer to the original state, such as bamboo-wave CAF [31], under the present conditions it results in a non-physical saturated state, specifically the wavy stratified flow shown here. However, increasing the pipe length allows the system to evolve into a physically realizable state, namely slug flow [12].…”

“…Magaletti et al [22] suggested P e = 1/(3Cn). In our previous work [31], we showed that a smaller pre-factor allows for larger time-step sizes without sacrificing accuracy. In this work, we employed P e = 1/(9.27Cn) in all simulations.…”

“…In laboratory experiments, the oil is usually injected concentrically at a prescribed flow rate Q o in a pipe in which water flows at rate Q w [5]. In our numerical method [31], we employ periodic boundary conditions in the axial direction. Axially periodic pipes do not suffer from end effects and enable the efficient simulation of fully developed flows in relatively short domains (provided that they are not shorter than the typical axial wavelength of the dominant flow pattern).…”

“…Consequently, the number of radial grid points was correspondingly reduced to n r = 96. The time-step size was kept in the range ∆t = [5•10 −5 −5•10 −4 ] to ensure that the fast interface dynamics were properly captured [31]. The error in the basic flow remained small, ||L2||,Cn=0.01 = 0.030.…”

Cahn-Hilliard Navier-Stokes simulations for marine free-surface flows

“…Some authors rearrange this definition into an apparent pressure term and a term involving the chemical potential gradient (Song et al, 2019), i.e., ST ( ) .…”