Abstract
This article proposes a numerical resolution of a one-dimensional (1D), transient, simplified two-fluid model regularized with an artificial diffusion term for modeling stratified, wavy and slug flow in horizontal and nearly horizontal pipes. Artificial diffusion is introduced to prevent the unbounded growth of instabilities where the 1D two-fluid model is ill-posed. We propose a method to set the artificial diffusion case by case to obtain the desired cut-off at short wavelengths by combining the choice of the spatial discretisation and the amplification factors obtained by the linear stability analysis of the model. A proper criterion to simulate two-phase to single-phase flow transition, which occurs during slug formation, is also developed. Flow pattern transitions have been numerically computed and compared against theoretical transition boundaries and experimental observations. Moreover, we showed that the developed code computes slug initiation and slug characteristics, in a reasonably accurate way considering the simplicity of the model, comparing numerical results with well-known empirical correlations and experimental data. Furthermore, the model simplicity leads to a computationally-inexpensive numerical resolution; this can be useful in engineering applications where obtaining fast numerical results is fundamental, such as applications involving automated control for two-phase flows.
Highlights
The numerical method presented in [23] has been properly modified to account for the transition from two-phase to single-phase flow, which occurs during slug formation; we remark that, without this method, this approach would be applicable only in stratified and wavy flow and would be unable to describe slug flow; see Section 3.1
We adopted a simplified two-fluid model regularized with artificial diffusion, to deal with the issue of ill-posedness
An original numerical procedure to describe the two-phase to single-phase flow transition was designed and implemented, thanks to which the numerical code is able to simulate the slug flow regime, as well as smooth and wavy stratified flow
Summary
Slug flow is a highly intermittent flow regime (liquid slugs are followed by large gas bubbles at a randomly fluctuating frequency [1,2]) typical of many engineering applications, such as petroleum transport pipelines, chemical and nuclear industries and buoyancy-driven fermentation devices [3].This flow pattern may arise in horizontal and slightly inclined pipes from stratified flow because of the growth of instabilities: small perturbations appear on the liquid surface, and some may grow into larger waves to fill the pipe completely due to the well-known Kelvin–Helmholtz instability [4,5,6].Slug flow can be established due to pipe slope changes, i.e., when the pipe inclination, initially horizontal or downward, turns upward: in this case, the liquid accumulates because of gravity, and the liquid volume fraction increases until the stratified-slug flow transition occurs [7].In the past few decades, many numerical codes have been developed to numerically describe slug flow and to compute slugs’ characteristics; one of the first methods was the ‘unit-cell’ approach, which enables a steady-state analysis of a control volume for gas bubbles and liquid slugs [8,9,10].Issa and Kempf [11] pointed out that “unit-cell” models cannot predict flow pattern transitions; steady-state models are not necessarily capable of predicting slug flow initiation in inclinedEnergies 2017, 10, 1372; doi:10.3390/en10091372 www.mdpi.com/journal/energiesEnergies 2017, 10, 1372 pipes due to liquid accumulation. Slug flow is a highly intermittent flow regime (liquid slugs are followed by large gas bubbles at a randomly fluctuating frequency [1,2]) typical of many engineering applications, such as petroleum transport pipelines, chemical and nuclear industries and buoyancy-driven fermentation devices [3] This flow pattern may arise in horizontal and slightly inclined pipes from stratified flow because of the growth of instabilities: small perturbations appear on the liquid surface, and some may grow into larger waves to fill the pipe completely due to the well-known Kelvin–Helmholtz instability [4,5,6]. The second method is slug tracking: each single slug is tracked, i.e., the position of every slug tail and of every slug front is followed along the pipe using Lagrangian coordinates, and mass and momentum transport equations are solved at the slug front and tail This approach was implemented in the commercial code OLGA, Oil and Gas simulator [15] and by Kjeldby et al [16]. Slug formation, growth and decay arise naturally from the numerical solution of the two-fluid model for stratified flow, without introducing special correlations or other constraints
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